Papers 2024

• The phase diagram of quantum chromodynamics in one dimension on a quantum computer

  Anton T. Than, Yasar Y. Atas, Abhijit Chakraborty, Jinglei Zhang, Matthew T. Diaz, Kalea Wen, Xingxin Liu, Randy Lewis, Alaina M. Green, Christine A. Muschik, Norbert M. Linke

  arXiv:2501.00579 · December 31, 2024 · quant-ph · Nature Communications 16, 10288 (2025) · doi

  Abstract

  The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behavior of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce color-neutrality constraints. This work marks the first lattice gauge theory quantum simulation of QCD at finite density and temperature for two and three colors, laying the foundation to explore QCD phenomena on quantum platforms.

• Temporally localized quantum operations on continuous-wave thermal light

  Yunkai Wang, Yujie Zhang, Virginia O. Lorenz

  arXiv:2412.17223 · December 23, 2024 · quant-ph

  Abstract

  Previous work showed that thermal light with a blackbody spectrum cannot be decomposed into a mixture of independent localized pulses. However, we find that in the weak-source limit and under the assumption of a flat spectrum, the first non-vacuum term in the state expansion does form a mixture of such pulses. This decomposition is essential for quantum-enhanced astronomical interferometry, which typically operates on localized pulses even though stellar light is inherently continuous-wave. We present a quantum derivation of the van Cittert-Zernike theorem that incorporates finite bandwidth, thereby justifying the operations on localized pulses while processing continuous-wave thermal light. For general spectra in the weak-source limit, we establish a criterion under which correlations between pulses can be safely neglected. When this criterion is not met, we provide a corrected strategy that accurately accounts for both the spectral profile and the detector-defined pulse shape.

• Information scrambling and entanglement dynamics in Floquet Time Crystals

  Himanshu Sahu, Fernando Iemini

  arXiv:2411.13469 · November 20, 2024 · quant-ph · Phys. Rev. B 111, 104302 (2025) · doi

  Abstract

  We study the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement of entropy as quantitative measures of information propagation in disordered many-body systems exhibiting Floquet time-crystal (FTC) phases. We find that OTOC spreads in the FTC with different characteristic timescales due to the existence of a preferred ``quasi-protected'' direction - denoted as $\ell$-bit direction - along which the spins stabilize their period-doubling magnetization for exponentially long times. While orthogonal to this direction the OTOC thermalizes as an usual MBL time-independent system (at stroboscopic times), along the $\ell$-bit direction the system features a more complex structure. The scrambling appears as a combination of an initially frozen dynamics (while in the stable period doubling magnetization time window) and a later logarithmic slow growth (over its decoherence regime) till full thermalization. Interestingly, in the late time regime, since the wavefront propagation of correlations has already settled through the whole chain, scrambling occurs at the same rate regardless of the distance between the spins, thus resulting in an overall envelope-like structure of all OTOCs, independent of their distance, merging into a single growth. Alongside, the entanglement entropy shows a logarithmic growth over all time, reflecting the slow dynamics up to a thermal volume-law saturation.

• Cryptographic tests of the python's lunch conjecture

  Alex May, Sabrina Pasterski, Chris Waddell, Michelle Xu

  arXiv:2411.10527 · November 15, 2024 · hep-th · SciPost Phys. 19, 084 (2025) · doi

  Abstract

  In the AdS/CFT correspondence, a subregion of the CFT allows for the recovery of a corresponding subregion of the bulk known as its entanglement wedge. In some cases, an entanglement wedge contains a locally but not globally minimal surface homologous to the CFT subregion, in which case it is said to contain a python's lunch. It has been proposed that python's lunch geometries should be modelled by tensor networks that feature projective operations where the wedge narrows. This model leads to the python's lunch (PL) conjecture, which asserts that reconstructing information from past the locally minimal surface is computationally difficult. In this work, we use cryptographic tools related to a primitive known as the Conditional Disclosure of Secrets (CDS) to develop consequences of the projective tensor network model that can be checked directly in AdS/CFT. We argue from the tensor network picture that the mutual information between appropriate CFT subregions is lower bounded linearly by an area difference associated with the geometry of the lunch. Recalling that the mutual information is also computed by bulk extremal surfaces, this gives a checkable geometrical consequence of the tensor network model. We prove weakened versions of this geometrical statement in asymptotically AdS$_{2+1}$ spacetimes satisfying the null energy condition, and confirm it in some example geometries, supporting the tensor network model and by proxy the PL conjecture.

• Quantum state preparation with optimal T-count

  David Gosset, Robin Kothari, Kewen Wu

  arXiv:2411.04790 · November 7, 2024 · quant-ph · Quantum 10, 2168 (2026) · doi

  Abstract

  How many T gates are needed to approximate an arbitrary $n$-qubit quantum state to within error $\varepsilon$? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is $Θ\left(\sqrt{2^n\log(1/\varepsilon)}+\log(1/\varepsilon)\right)$ if we allow ancilla qubits. We also show that this is the optimal T-count for implementing an arbitrary diagonal $n$-qubit unitary to within error $\varepsilon$. We describe applications in which a tensor product of many single-qubit unitaries can be synthesized in parallel for the price of one.

• Does connected wedge imply distillable entanglement?

  Takato Mori, Beni Yoshida

  arXiv:2411.03426 · November 5, 2024 · hep-th · JHEP 01 (2026) 125 · doi

  Abstract

  The Ryu-Takayanagi formula predicts that two boundary subsystems $A$ and $C$ can exhibit large mutual information $I(A:C)$ even when they are spatially disconnected on the boundary and separated by a buffer subsystem $B$, as long as $A$ and $C$ have connected entanglement wedge in the bulk. However, whether the reduced state $ρ_{AC}$ contains distillable EPR pairs has remained a longstanding open problem. In this work, we resolve this problem by showing that: i) there is no LO-distillable entanglement at leading order in $G_N$, suggesting the absence of bipartite entanglement in a holographic mixed state $ρ_{AC}$, and ii) one-shot, one-way LOCC-distillable entanglement is given at leading order by locally accessible information $J^W(A|C)$, which is related to the entanglement wedge cross section $E^W$ involving the (third) purifying system $B$ via $J^W(A|C) = S_A - E^W(A:B)$. Namely, we demonstrate that a connected entanglement wedge does not necessarily imply nonzero distillable entanglement in one-shot, one-way LOCC. We also show that entanglement of formation $E_{F}(A:C)$ is given by $E^W(A:C)$ at leading order in holography.

• Random Distillation Protocols in Long Baseline Telescopy

  Yunkai Wang, Eric Chitambar

  arXiv:2411.02678 · November 4, 2024 · quant-ph · doi

  Abstract

  In quantum-enhanced astronomical imaging, multiple distant apertures work together by utilizing quantum resources distributed from a central server. Our findings suggest that pre-processing the stellar light received by all telescopes can improve imaging performance without increasing resource consumption. The pre-processing leverages weak quantum measurements and modifies random-party entanglement distillation protocols from quantum information science. Intuitively, this approach allows us to collapse the stellar light that is originally coherent between all telescopes to one pair of telescopes with probability arbitrarily close to one. The central server can then distribute entanglement solely to the pair of telescopes receiving a photon, thereby enhancing the efficiency of resource utilization. We discuss two types of resources that benefit from this pre-processing: shared entanglement and a shared reference frame.

• The horocycle regulator: exact cutoff-independence in AdS/CFT

  Sristy Agrawal, Oliver DeWolfe, Kenneth Higginbotham, Joshua Levin

  arXiv:2410.00950 · October 1, 2024 · hep-th

  Abstract

  While the entanglement entropy of a single subregion in quantum field theory is formally infinite and requires regularization, certain combinations of entropies are perfectly finite in the limit that the regulator is removed, the mutual information being a common example. For generic regulator schemes, such as a holographic calculation with a uniform radial cutoff, these quantities show non-trivial dependence on the regulator at finite values of the cutoff. We investigate a holographic regularization scheme defined in three-dimensional anti-de Sitter space constructed from \textit{horocycles}, curves in two-dimensional hyperbolic space perpendicular to all geodesics approaching a single point on the boundary, that leads to finite information measures that are \textit{totally} cutoff-independent, even at finite values of the regulator. We describe a broad class of such information measures, and describe how the field theory dual to the horocycle regulator is inherently non-local.

• Pure state entanglement and von Neumann algebras

  Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, Henrik Wilming

  arXiv:2409.17739 · September 26, 2024 · quant-ph · doi

  Abstract

  We develop the theory of local operations and classical communication (LOCC) for bipartite quantum systems represented by commuting von Neumann algebras. Our central result is the extension of Nielsen's Theorem, stating that the LOCC ordering of bipartite pure states is equivalent to the majorization of their restrictions, to arbitrary factors. As a consequence, we find that in bipartite system modeled by commuting factors in Haag duality, a) all states have infinite single-shot entanglement if and only if the local factors are not of type I, b) type III factors are characterized by LOCC transitions of arbitrary precision between any two pure states, and c) the latter holds even without classical communication for type III$_{1}$ factors. In the case of semifinite factors, the usual construction of pure state entanglement monotones carries over. Together with recent work on embezzlement of entanglement, this gives a one-to-one correspondence between the classification of factors into types and subtypes and operational entanglement properties. In the appendix, we provide a self-contained treatment of majorization on semifinite von Neumann algebras and $σ$-finite measure spaces.

• Multipartite Embezzlement of Entanglement

  Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2409.07646 · September 11, 2024 · quant-ph · Quantum 9, 1818 (2025) · doi

  Abstract

  Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via local operations and without communication while perturbing the resource arbitrarily little. Recently, the existence of embezzling states of bipartite systems of type III von Neumann algebras was shown. However, both the multipartite case and the precise relation between embezzling states and the notion of embezzling families, as originally defined by van Dam and Hayden, was left open. Here, we show that finite-dimensional approximations of multipartite embezzling states form multipartite embezzling families. In contrast, not every embezzling family converges to an embezzling state. We identify an additional consistency condition that ensures that an embezzling family converges to an embezzling state. This criterion distinguishes the embezzling family of van Dam and Hayden from the one by Leung, Toner, and Watrous. The latter generalizes to the multipartite setting. By taking a limit, we obtain a multipartite system of commuting type III$_1$ factors on which every state is an embezzling state. We discuss our results in the context of quantum field theory and quantum many-body physics. As open problems, we ask whether vacua of relativistic quantum fields in more than two spacetime dimensions are multipartite embezzling states and whether multipartite embezzlement allows for an operator-algebraic characterization.

• Solving Free Fermion Problems on a Quantum Computer

  Maarten Stroeks, Daan Lenterman, Barbara Terhal, Yaroslav Herasymenko

  arXiv:2409.04550 · September 6, 2024 · quant-ph · Physical Review Research 7 (4), 043176 (2025) · doi

  Abstract

  Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often moderate, these costs can be prohibitive in practice when large systems are considered. We present several free-fermion problems that can be solved by a quantum algorithm with substantially reduced computational costs. The memory costs are exponentially improved, poly log$(N)$. The runtime improvement, compared to the best known classical algorithms, is either exponential or significantly polynomial, depending on the geometry of the problem. The simulation of free-fermion dynamics belongs to the BQP-hard complexity class. This implies (under standard assumptions) that our algorithm yields an exponential speedup for any classical algorithm at least for some geometries. The key technique in our algorithm is the block-encoding of objects such as correlation matrices and Green's functions into a unitary. We demonstrate how such unitaries can be efficiently realized as quantum circuits, in the context of dynamics and thermal states of tight-binding Hamiltonians. The special cases of disordered and inhomogeneous lattices, as well as large non-lattice graphs, are presented in detail. Finally, we show that our simulation algorithm generalizes to other promising targets, including free boson systems.

• Quantum complexity and localization in random and time-periodic unitary circuits

  Himanshu Sahu, Aranya Bhattacharya, Pingal Pratyush Nath

  arXiv:2409.03656 · September 5, 2024 · quant-ph · Phys. Rev. B 113, 214312 (2026) · doi

  Abstract

  We study the growth and saturation of complexity in Krylov basis in random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, this notion of complexity grows linearly before saturating at a late-time value of $d/2$, where $d$ is the Hilbert space dimension, at timescales $\sim d$. Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits. In brick-wall case, complexity in Krylov basis exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of the complexity enabling us to probe the transition between thermal and many-body localized phases.

• Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation

  Santanu Bosu Antu, Sisi Zhou

  arXiv:2408.11101 · August 20, 2024 · quant-ph · Quantum 9, 1766 (2025) · doi

  Abstract

  Estimating many-body Hamiltonians has wide applications in quantum technology. By allowing coherent evolution of quantum systems and entanglement across multiple probes, the precision of estimating a fully connected $k$-body interaction can scale up to $(n^kt)^{-1}$, where $n$ is the number of probes and $t$ is the probing time. However, the optimal scaling may no longer be achievable under quantum noise, and it is important to apply quantum error correction in order to recover this limit. In this work, we study the performance of stabilizer quantum error correcting codes in estimating many-body Hamiltonians under noise. When estimating a fully connected $ZZZ$ interaction under single-qubit noise, we showcase three families of stabilizer codes -- thin surface codes, quantum Reed--Muller codes and Shor codes -- that achieve the scalings of $(nt)^{-1}$, $(n^2t)^{-1}$ and $(n^3t)^{-1}$, respectively, all of which are optimal with $t$. We further discuss the relation between stabilizer structure and the scaling with $n$, and identify several no-go theorems. For instance, we find codes with constant-weight stabilizer generators can at most achieve the $n^{-1}$ scaling, while the optimal $n^{-3}$ scaling is achievable if and only if the code bears a repetition code substructure, like in Shor code.

• Local quantum channels giving rise to quasi-local Gibbs states

  Itai Arad, Raz Firanko, Omer Gurevich

  arXiv:2408.08672 · August 16, 2024 · quant-ph

  Abstract

  We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated application of these channels can be seen as a simple model for the thermalization process of a many-body system. We study its steady state perturbatively, by interpolating between the 1-local and 2-local channels with a perturbation parameter $ε$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $ε$, we show that the $k$'th order term corresponds to a $(k+1)$-local interaction term in the Hamiltonian, which follows the same interaction graph as the Kraus channel. We also prove a complementary result suggesting the existence of an interaction strength threshold, under which the total weight of the high-order terms in the Hamiltonian decays exponentially fast. For sufficiently small $ε$, this implies both exponential decay of local correlation functions and a classical algorithm for computing expectation value of local observables in such steady states. Finally, we present numerical simulations of various channels that support our theoretical results.

• Small correlation is sufficient for optimal noisy quantum metrology

  Chao Yin, Victor V. Albert, Sisi Zhou

  arXiv:2408.00079 · July 31, 2024 · quant-ph · Quantum 10, 2050 (2026) · doi

  Abstract

  We propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit on-site measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Finally, we show that spin squeezed states are also optimal for noisy metrology under general conditions.

• Quantum advantage from measurement-induced entanglement in random shallow circuits

  Adam Bene Watts, David Gosset, Yinchen Liu, Mehdi Soleimanifar

  arXiv:2407.21203 · July 30, 2024 · quant-ph

  Abstract

  We study random constant-depth quantum circuits in a two-dimensional architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the qubits of the output state. It is conjectured that this long-range measurement-induced entanglement (MIE) proliferates when the circuit depth is at least a constant critical value. For circuits composed of Haar-random two-qubit gates, it is also believed that this coincides with a quantum advantage phase transition in the classical hardness of sampling from the output distribution. Here we provide evidence for a quantum advantage phase transition in the setting of random Clifford circuits. Our work extends the scope of recent separations between the computational power of constant-depth quantum and classical circuits, demonstrating that this kind of advantage is present in canonical random circuit sampling tasks. In particular, we show that in any architecture of random shallow Clifford circuits, the presence of long-range MIE gives rise to an unconditional quantum advantage. In contrast, any depth-d 2D quantum circuit that satisfies a short-range MIE property can be classically simulated efficiently and with depth O(d). Finally, we introduce a two-dimensional, depth-2, "coarse-grained" circuit architecture, composed of random Clifford gates acting on O(log n) qubits, for which we prove the existence of long-range MIE and establish an unconditional quantum advantage.

• Convergence Rates for the Trotter Splitting for Unbounded Operators

  Simon Becker, Niklas Galke, Robert Salzmann, Lauritz van Luijk

  arXiv:2407.04045 · July 4, 2024 · math-ph · Foundations of Computational Mathematics (2025) · doi

  Abstract

  We study convergence rates of the Trotter splitting $e^{A+L} = \lim_{n \to \infty} (e^{L/n} e^{A/n})^n$ in the strong operator topology. In the first part, we use complex interpolation theory to treat generators $L$ and $A$ of contraction semigroups on Banach spaces, with $L$ relatively $A$-bounded. In the second part, we study unitary dynamics on Hilbert spaces and develop a new technique based on the concept of energy constraints. Our results provide a complete picture of the convergence rates for the Trotter splitting for all common types of Schrödinger and Dirac operators, including singular, confining and magnetic vector potentials, as well as molecular many-body Hamiltonians in dimension $d=3$. Using the Brezis-Mironescu inequality, we derive convergence rates for the Schrödinger operator with $V(x)=\pm |x|^{-a}$ potential. In each case, our conditions are fully explicit.

• Tensor networks for black hole interiors: non-isometries, quantum extremal surfaces, and wormholes

  Gracemarie Bueller, Oliver DeWolfe, Kenneth Higginbotham

  arXiv:2407.01666 · July 1, 2024 · hep-th

  Abstract

  We use hyperbolic tensor networks to construct a holographic map for black hole interiors that adds a notion of locality to the non-isometric codes proposed by Akers, Engelhardt, Harlow, Penington, and Vardhan. We use tools provided by these networks to study the relationship between non-isometries and quantum extremal surfaces behind the horizon. Furthermore, we introduce a limited notion of dynamics for these interior tensor networks based on the qudit models introduced by Akers et al., and study the evolution of quantum extremal surfaces in an evaporating black hole. We also find a tensor network description of a wormhole connecting the black hole interior to the radiation, providing a mechanism for interior states and operators to be encoded in the radiation after the Page time. As a particular case, we construct a tensor network realization of the backwards-forwards maps recently proposed to incorporate non-trivial effective dynamics in dynamical constructions of these non-isometric black hole codes.

• qLUE: A Quantum Clustering Algorithm for Multi- Dimensional Datasets

  Dhruv Gopalakrishnan, Luca Dellantonio, Antonio Di Pilato, Wahid Redjeb, Felice Pantaleo, Michele Mosca

  arXiv:2407.00357 · June 29, 2024 · quant-ph

  Abstract

  Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges stemming from datasets that span more spatial dimensions. In fact, the best-performing clustering algorithms scale linearly in the number of points, but quadratically with respect to the local density of points. In this work, we introduce qLUE, a quantum clustering algorithm that scales linearly in both the number of points and their density. qLUE is inspired by CLUE, an algorithm developed to address the challenging time and memory budgets of Event Reconstruction (ER) in future High-Energy Physics experiments. As such, qLUE marries decades of development with the quadratic speedup provided by quantum computers. We numerically test qLUE in several scenarios, demonstrating its effectiveness and proving it to be a promising route to handle complex data analysis tasks -- especially in high-dimensional datasets with high densities of points.

• Quantum reservoir computing using the stabilizer formalism for encoding classical data

  Franz G. Fuchs, Alexander J. Stasik, Stanley Miao, Ola Tangen Kulseng, Ruben Pariente Bassa

  arXiv:2407.00445 · June 29, 2024 · quant-ph

  Abstract

  Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main contribution is a generalization of the standard way to robustly en- and decode time series into subspaces defined by the cosets of a given stabilizer. A key observation is the necessity to perform the decoding step, which in turn ensures a consistent way of encoding. This provides a systematic way to encode classical information in a robust way. We provide a numerical analysis on a discrete time series given by two standard maps, namely the logistic and the Hénon map. Our numerical findings indicate that the system's performance is increasing with the length of the training data.

• NAC-QFL: Noise Aware Clustered Quantum Federated Learning

  Himanshu Sahu, Hari Prabhat Gupta

  arXiv:2406.14236 · June 20, 2024 · quant-ph

  Abstract

  Recent advancements in quantum computing, alongside successful deployments of quantum communication, hold promises for revolutionizing mobile networks. While Quantum Machine Learning (QML) presents opportunities, it contends with challenges like noise in quantum devices and scalability. Furthermore, the high cost of quantum communication constrains the practical application of QML in real-world scenarios. This paper introduces a noise-aware clustered quantum federated learning system that addresses noise mitigation, limited quantum device capacity, and high quantum communication costs in distributed QML. It employs noise modelling and clustering to select devices with minimal noise and distribute QML tasks efficiently. Using circuit partitioning to deploy smaller models on low-noise devices and aggregating similar devices, the system enhances distributed QML performance and reduces communication costs. Leveraging circuit cutting, QML techniques are more effective for smaller circuit sizes and fidelity. We conduct experimental evaluations to assess the performance of the proposed system. Additionally, we introduce a noisy dataset for QML to demonstrate the impact of noise on proposed accuracy.

• Critical Fermions are Universal Embezzlers

  Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2406.11747 · June 17, 2024 · quant-ph · Nature Physics 21, 1141-1146 (2025) · doi

  Abstract

  Universal embezzlers are bipartite quantum systems from which any entangled state may be extracted to arbitrary precision using local operations while perturbing the state of the system arbitrarily little. Here, we show that universal embezzlers are ubiquitous in many-body physics: The ground state sector of every local, translation-invariant, and critical free-fermionic many-body system on a one-dimensional lattice is a universal embezzler if bi-partitioned into two half-chains. The same property holds in locally-interacting, dual spin chains via the Jordan-Wigner transformation. Universal embezzlement manifests already for finite system sizes, not only in the thermodynamic limit: For any finite error and any targeted entangled state, a finite length of the chain is sufficient to embezzle said state within the given error. On a technical level, our main result establishes that the half-chain observable algebras associated with ground state sectors of the given models are type III$_1$ factors.

• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity

  Himanshu Sahu

  arXiv:2406.05865 · June 9, 2024 · quant-ph · Phys. Rev. A 110, 052405 (2024) · doi

  Abstract

  We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a probe of information scrambling. The OTOC for local spin operators in all directions has a light-cone structure which is ``shell-like''. As the wavefront passes, the OTOC approaches to zero in the long-time limit, showing no signature of scrambling. The introduction of spatial or temporal disorder changes the shape of the light-cone akin to localization of wavefunction. We formulate the K-complexity in system with discrete-time evolution, and show that it grows linearly in discrete-time quantum walk. The presence of disorder modifies this growth to sub-linear. Our study present interesting case to explore many-body phenomenon in a discrete-time quantum walk using scrambling.

• Holographic motivations and observational evidence for decreasing dark energy

  Mark Van Raamsdonk, Chris Waddell

  arXiv:2406.02688 · June 4, 2024 · hep-th

  Abstract

  Negative lambda gravitational effective field theories dual to holographic CFTs have potentially realistic cosmological solutions. Generic cosmological solutions of these effective field theories have scalar field evolution that can lead to a period of accelerated expansion when the scalar field is at positive values of its potential (Fig. 1). If such a model describes our universe, significant evolution of dark energy is expected over a Hubble time as the scalar descends from positive to negative values of its potential towards the AdS extremum. Our recent observational study 2305.04946 based on supernova and baryon acoustic oscillation (BAO) observations suggests that significant evolution of dark energy associated with a descending scalar field may be preferred by data (Fig. 2). Taking a linear approximation to the scalar potential around the present value, a standard likelihood analysis gives an $e^{- χ^2/2}$ distribution in which $dV/dt$ is presently negative in $99.99 \%$ of the distribution, with a mean fractional variation of the potential of $36 \%$ over the period $z \lessapprox 2$ over which supernova data is available. In this note, we review these theoretical and observational results and provide an update on the question of how the physics of these cosmological solutions can be related to the physics of the underlying CFT.

• Improving the Fidelity of CNOT Circuits on NISQ Hardware

  Dohun Kim, Minyoung Kim, Sarah Meng Li, Michele Mosca

  arXiv:2405.19891 · May 30, 2024 · quant-ph

  Abstract

  We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler, it improves the fidelity of a synthesized CNOT circuit by about 2 times on average (up to 9 times). It lowers the synthesized CNOT count by a factor of 13 on average (up to a factor of 162). Our contribution is twofold. First, we define a $\textsf{Cost}$ function by approximating the average gate fidelity $F_{avg}$. According to the simulation results, $\textsf{Cost}$ fits the error probability of a noisy CNOT circuit, $\textsf{Prob} = 1 - F_{avg}$, much tighter than the commonly used cost functions. On IBM's fake Nairobi backend, it matches $\textsf{Prob}$ to within $10^{-3}$. On other backends, it fits $\textsf{Prob}$ to within $10^{-1}$. $\textsf{Cost}$ accurately quantifies the dynamic error characteristics and shows remarkable scalability. Second, we propose a noise-aware CNOT routing algorithm, NAPermRowCol, by adapting the leading Steiner-tree-based connectivity-aware CNOT synthesis algorithms. A weighted edge is used to encode a CNOT gate error rate and $\textsf{Cost}$-instructed heuristics are applied to each reduction step. NAPermRowCol does not use ancillary qubits and is not restricted to certain initial qubit maps. Compared with algorithms that are noise-agnostic, it improves the fidelity of a synthesized CNOT circuit across varied NISQ hardware. Depending on the benchmark circuit and the IBM backend selected, it lowers the synthesized CNOT count up to $56.95\%$ compared to ROWCOL and up to $21.62\%$ compared to PermRowCol. It reduces the synthesis $\textsf{Cost}$ up to $25.71\%$ compared to ROWCOL and up to $9.12\%$ compared to PermRowCol. Our method can be extended to route a more general quantum circuit, giving a powerful new tool for compiling on NISQ devices.

• Energy-limited quantum dynamics

  Lauritz van Luijk

  arXiv:2405.10259 · May 16, 2024 · quant-ph · Commun. Math. Phys. 406, 120 (2025) · doi

  Abstract

  We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce a finite amount of energy to the system, and continuous-time dynamics only increase the energy gradually over time. We systematically study such "energy-limited" channels and dynamics. For Markovian dynamics, energy-limitedness is equivalent to a single operator inequality in the Heisenberg picture. We observe new submultiplicativity inequalities for the energy-constrained diamond and operator norms and use them to derive new state-dependent continuity bounds for quantum speed limits.

• How Much Entanglement Is Needed for Topological Codes and Mixed States with Anomalous Symmetry?

  Zhi Li, Dongjin Lee, Beni Yoshida

  arXiv:2405.07970 · May 13, 2024 · quant-ph · Phys. Rev. X 15, 021090 (2025)

  Abstract

  It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM), which quantifies the maximal overlap between a given state and any short-range-entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our analysis establishes an intriguing link between quantum anomaly and entanglement: A quantum state respecting anomalous 1-form symmetries, must be long-range-entangled and have large GEM. Our results also extend to mixed states, such as the $ZX$-dephased toric code, providing a provably nontrivial class of intrinsically mixed-state phases.

• How much entanglement is needed for quantum error correction?

  Sergey Bravyi, Dongjin Lee, Zhi Li, Beni Yoshida

  arXiv:2405.01332 · May 2, 2024 · quant-ph · Phys. Rev. Lett. 134, 210602 (2025) · doi

  Abstract

  It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this belief depends on the specific code and the choice of entanglement measure. To this end, we characterize a tradeoff between the code distance $d$ quantifying the number of correctable errors, and the geometric entanglement measure of logical states quantifying their maximal overlap with product states or more general ``topologically trivial" states. The maximum overlap is shown to be exponentially small in $d$ for three families of codes: (1) low-density parity check codes with commuting check operators, (2) stabilizer codes, and (3) codes with a constant encoding rate. Equivalently, the geometric entanglement of any logical state of these codes grows at least linearly with $d$. On the opposite side, we also show that this distance-entanglement tradeoff does not hold in general. For any constant $d$ and $k$ (number of logical qubits), we show there exists a family of codes such that the geometric entanglement of some logical states approaches zero in the limit of large code length.

• Triply efficient shadow tomography

  Robbie King, David Gosset, Robin Kothari, Ryan Babbush

  arXiv:2404.19211 · April 30, 2024 · quant-ph · PRX Quantum 6, 010336 (2025) · doi

  Abstract

  Given copies of a quantum state $ρ$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $ε$. We say that a shadow tomography protocol is triply efficient if it is sample- and time-efficient, and only employs measurements that entangle a constant number of copies of $ρ$ at a time. The classical shadows protocol based on random single-copy measurements is triply efficient for the set of local Pauli observables. This and other protocols based on random single-copy Clifford measurements can be understood as arising from fractional colorings of a graph $G$ that encodes the commutation structure of the set of observables. Here we describe a framework for two-copy shadow tomography that uses an initial round of Bell measurements to reduce to a fractional coloring problem in an induced subgraph of $G$ with bounded clique number. This coloring problem can be addressed using techniques from graph theory known as chi-boundedness. Using this framework we give the first triply efficient shadow tomography scheme for the set of local fermionic observables, which arise in a broad class of interacting fermionic systems in physics and chemistry. We also give a triply efficient scheme for the set of all $n$-qubit Pauli observables. Our protocols for these tasks use two-copy measurements, which is necessary: sample-efficient schemes are provably impossible using only single-copy measurements. Finally, we give a shadow tomography protocol that compresses an $n$-qubit quantum state into a $\text{poly}(n)$-sized classical representation, from which one can extract the expected value of any of the $4^n$ Pauli observables in $\text{poly}(n)$ time, up to a small constant error.

• Holographic scattering and non-minimal RT surfaces

  Jacqueline Caminiti, Batia Friedman-Shaw, Alex May, Robert C. Myers, Olga Papadoulaki

  arXiv:2404.15400 · April 23, 2024 · hep-th · JHEP 10 (2024) 119 · doi

  Abstract

  In the AdS/CFT correspondence, the causal structure of the bulk AdS spacetime is tied to entanglement in the dual CFT. This relationship is captured by the connected wedge theorem, which states that a bulk scattering process implies the existence of $O(1/G_N)$ entanglement between associated boundary subregions. In this paper, we study the connected wedge theorem in two asymptotically AdS$_{2+1}$ spacetimes: the conical defect and BTZ black hole geometries. In these settings, we find that bulk scattering processes require not just large entanglement, but also additional restrictions related to candidate RT surfaces which are non-minimal. We argue these extra relationships imply a certain CFT entanglement structure involving internal degrees of freedom. Because bulk scattering relies on sub-AdS scale physics, this supports the idea that sub-AdS scale locality emerges from internal degrees of freedom. While the new restriction that we identify on non-minimal surfaces is stronger than the initial statement of the connected wedge theorem, we find that it is necessary but still not sufficient to imply bulk scattering in mixed states.

• Conditional disclosure of secrets with quantum resources

  Vahid R. Asadi, Kohdai Kuroiwa, Debbie Leung, Alex May, Sabrina Pasterski, Chris Waddell

  arXiv:2404.14491 · April 22, 2024 · quant-ph · Quantum 9, 1885 (2025) · doi

  Abstract

  The conditional disclosure of secrets (CDS) primitive is among the simplest cryptographic settings in which to study the relationship between communication, randomness, and security. CDS involves two parties, Alice and Bob, who do not communicate but who wish to reveal a secret $z$ to a referee if and only if a Boolean function $f$ has $f(x,y)=1$. Alice knows $x,z$, Bob knows $y$, and the referee knows $x,y$. Recently, a quantum analogue of this primitive called CDQS was defined and related to $f$-routing, a task studied in the context of quantum position-verification. CDQS has the same inputs, outputs, and communication pattern as CDS but allows the use of shared entanglement and quantum messages. We initiate the systematic study of CDQS, with the aim of better understanding the relationship between privacy and quantum resources in the information theoretic setting. We begin by looking for quantum analogues of results already established in the classical CDS literature. Doing so we establish a number of basic properties of CDQS, including lower bounds on entanglement and communication stated in terms of measures of communication complexity. Because of the close relationship to the $f$-routing position-verification scheme, our results have relevance to the security of these schemes.

• Speed limits to the growth of Krylov complexity in open quantum systems

  Aranya Bhattacharya, Pingal Pratyush Nath, Himanshu Sahu

  arXiv:2403.03584 · March 6, 2024 · quant-ph · Phys. Rev. D 109, L121902 (2024) · doi

  Abstract

  Recently, the propagation of information through quantum many-body systems, developed to study quantum chaos, have found many application from black holes to disordered spin systems. Among other quantitative tools, Krylov complexity has been explored as a diagnostic tool for information scrambling in quantum many-body systems. We introduce a universal limit to the growth of the Krylov complexity in dissipative open quantum systems by utilizing the uncertainty relation for non-hermitian operators. We also present the analytical results of Krylov complexity for characteristic behavior of Lanczos coefficients in dissipative systems. The validity of these results are demonstrated by explicit study of transverse-field Ising model under dissipative effects.

• Entanglement-enabled advantage for learning a bosonic random displacement channel

  Changhun Oh, Senrui Chen, Yat Wong, Sisi Zhou, Hsin-Yuan Huang, Jens A. H. Nielsen, Zheng-Hao Liu, Jonas S. Neergaard-Nielsen, Ulrik L. Andersen, Liang Jiang, John Preskill

  arXiv:2402.18809 · February 29, 2024 · quant-ph · Phys. Rev. Lett. 133, 230604 (2024) · doi

  Abstract

  We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on $n$ bosonic modes, called a random displacement channel. We prove that if the $n$ modes are not entangled with an ancillary quantum memory, then the channel must be sampled a number of times exponential in $n$ in order to estimate its characteristic function to reasonable precision; this lower bound on sample complexity applies even if the channel inputs and measurements performed on channel outputs are chosen adaptively. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of $n$, given a sufficient amount of squeezing. This establishes an exponential separation in sample complexity. We then analyze the effect of photon loss and show that the entanglement-assisted scheme is still significantly more efficient than any lossless entanglement-free scheme under mild experimental conditions. Our work illuminates the role of entanglement in learning continuous-variable systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms.

• Limits of noisy quantum metrology with restricted quantum controls

  Sisi Zhou

  arXiv:2402.18765 · February 29, 2024 · quant-ph · Physical Review Letters 133, 170801 (2024) · doi

  Abstract

  The Heisenberg limit (HL, with estimation error scales as $1/n$) and the standard quantum limit (SQL, $\propto 1/\sqrt{n}$) are two fundamental limits in estimating an unknown parameter in $n$ copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown though, whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this Letter, we discover various new limits for estimating qubit channels under restrictive controls. The HL is shown to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a single-qubit unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and for other cases a constant floor on the estimation error is proven. A practical example of the unitary protocol is provided.

• Efficient learning of quantum states prepared with few fermionic non-Gaussian gates

  Antonio Anna Mele, Yaroslav Herasymenko

  arXiv:2402.18665 · February 28, 2024 · quant-ph · PRX Quantum 6, 010319 (2025) · doi

  Abstract

  The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian and at most $t$ non-Gaussian gates. By Jordan-Wigner mapping, this also includes $n$-qubit states prepared by nearest-neighbour matchgate circuits with at most $t$ SWAP-gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is $\mathrm{poly}(n,2^t)$; thus if $t=O(\log(n))$, it is efficient. We also show that, if $t$ scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit compilation method.

• Linear gate bounds against natural functions for position-verification

  Vahid Asadi, Richard Cleve, Eric Culf, Alex May

  arXiv:2402.18648 · February 28, 2024 · quant-ph · Quantum 9, 1604 (2025) · doi

  Abstract

  A quantum position-verification scheme attempts to verify the spatial location of a prover. The prover is issued a challenge with quantum and classical inputs and must respond with appropriate timings. We consider two well-studied position-verification schemes known as $f$-routing and $f$-BB84. Both schemes require an honest prover to locally compute a classical function $f$ of inputs of length $n$, and manipulate $O(1)$ size quantum systems. We prove the number of quantum gates plus single qubit measurements needed to implement a function $f$ is lower bounded linearly by the communication complexity of $f$ in the simultaneous message passing model with shared entanglement. Taking $f(x,y)=\sum_i x_i y_i$ to be the inner product function, we obtain a $Ω(n)$ lower bound on quantum gates plus single qubit measurements. The scheme is feasible for a prover with linear classical resources and $O(1)$ quantum resources, and secure against sub-linear quantum resources.

• Rank lower bounds on non-local quantum computation

  Vahid R. Asadi, Eric Culf, Alex May

  arXiv:2402.18647 · February 28, 2024 · quant-ph

  Abstract

  A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, $f$-routing and $f$-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function $f(x,y)$ in terms of the rank of a matrix $g(x,y)$ whose entries are zero when $f(x,y)=0$, and strictly positive otherwise. This also leads to a lower bound on the Schmidt rank in terms of the non-deterministic quantum communication complexity of $f(x,y)$. Because of a relationship between $f$-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS.

• Randomly Monitored Quantum Codes

  Dongjin Lee, Beni Yoshida

  arXiv:2402.00145 · January 31, 2024 · quant-ph

  Abstract

  Quantum measurement has conventionally been regarded as the final step in quantum information processing, which is essential for reading out the processed information but collapses the quantum state into a classical state. However, recent studies have shown that quantum measurement itself can induce novel quantum phenomena. One seminal example is a monitored random circuit, which can generate long-range entanglement faster than a random unitary circuit. Inspired by these results, in this paper, we address the following question: When quantum information is encoded in a quantum error-correcting code, how many physical qubits should be randomly measured to destroy the encoded information? We investigate this question for various quantum error-correcting codes and derive the necessary and sufficient conditions for destroying the information through measurements. In particular, we demonstrate that for a large class of quantum error-correcitng codes, it is impossible to destroy the encoded information through random single-qubit Pauli measurements when a tiny portion of physical qubits is still unmeasured. Our results not only reveal the extraordinary robustness of quantum codes under measurement decoherence, but also suggest potential applications in quantum information processing tasks.

• Assessing the Benefits and Risks of Quantum Computers

  Travis L. Scholten, Carl J. Williams, Dustin Moody, Michele Mosca, William Hurley, William J. Zeng, Matthias Troyer, Jay M. Gambetta

  arXiv:2401.16317 · January 29, 2024 · quant-ph

  Abstract

  Quantum computing is an emerging technology with potentially far-reaching implications for national prosperity and security. Understanding the timeframes over which economic benefits and national security risks may manifest themselves is vital for ensuring the prudent development of this technology. To inform security experts and policy decision makers on this matter, we review what is currently known on the potential uses and risks of quantum computers, leveraging current research literature. The maturity of currently-available quantum computers is not yet at a level such that they can be used in production for large-scale, industrially-relevant problems, and they are not believed to currently pose security risks. We identify 2 large-scale trends -- new approximate methods (variational algorithms, error mitigation, and circuit knitting) and the commercial exploration of business-relevant quantum applications -- which, together, may enable useful and practical quantum computing in the near future. Crucially, these methods do not appear likely to change the required resources for cryptanalysis on currently-used cryptosystems. From an analysis we perform of the current and known algorithms for cryptanalysis, we find they require circuits of a size exceeding those that can be run by current and near-future quantum computers (and which will require error correction), though we acknowledge improvements in quantum algorithms for these problems are taking place in the literature. In addition, the risk to cybersecurity can be well-managed by the migration to new, quantum-safe cryptographic protocols, which we survey and discuss. Given the above, we conclude there is a credible expectation that quantum computers will be capable of performing computations which are economically-impactful before they will be capable of performing ones which are cryptographically-relevant.

• QuantumReservoirPy: A Software Package for Time Series Prediction

  Stanley Miao, Ola Tangen Kulseng, Alexander Stasik, Franz G. Fuchs

  arXiv:2401.10683 · January 19, 2024 · quant-ph

  Abstract

  In recent times, quantum reservoir computing has emerged as a potential resource for time series prediction. Hence, there is a need for a flexible framework to test quantum circuits as nonlinear dynamical systems. We have developed a software package to allow for quantum reservoirs to fit a common structure, similar to that of reservoirpy which is advertised as "a python tool designed to easily define, train and use (classical) reservoir computing architectures". Our package results in simplified development and logical methods of comparison between quantum reservoir architectures. Examples are provided to demonstrate the resulting simplicity of executing quantum reservoir computing using our software package.

• Entanglement cost for infinite-dimensional physical systems

  Hayata Yamasaki, Kohdai Kuroiwa, Patrick Hayden, Ludovico Lami

  arXiv:2401.09554 · January 17, 2024 · quant-ph · Commun. Math. Phys. 406, 277 (2025) · doi

  Abstract

  We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state $ρ_{AB}$ with finite quantum entropy on at least one of the subsystems $A$ or $B$. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure -- the entanglement cost -- for all infinite-dimensional physical systems.

• Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras

  Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, Henrik Wilming

  arXiv:2401.07299 · January 14, 2024 · math-ph

  Abstract

  We study the quantum information theoretic task of embezzlement of entanglement in the setting of von Neumann algebras. Given a shared entangled resource state, this task asks to produce arbitrary entangled states using local operations without communication while perturbing the resource arbitrarily little. We quantify the performance of a given resource state by the worst-case error. States for which the latter vanishes are 'embezzling states' as they allow to embezzle arbitrary entangled states with arbitrarily small error. The best and worst performance among all states defines two algebraic invariants for von Neumann algebras. The first invariant takes only two values. Either it vanishes and embezzling states exist, which can only happen in type III, or no state allows for nontrivial embezzlement. In the case of factors not of finite type I, the second invariant equals the diameter of the state space. This provides a quantitative operational interpretation of Connes' classification of type III factors within quantum information theory. Type III$_1$ factors are 'universal embezzlers' where every state is embezzling. Our findings have implications for relativistic quantum field theory, where type III algebras naturally appear. For instance, they explain the maximal violation of Bell inequalities in the vacuum. Our results follow from a one-to-one correspondence between embezzling states and invariant probability measures on the flow of weights. We also establish that universally embezzling ITPFI factors are of type III$_1$ by elementary arguments.

• Quantum chaos in PT symmetric quantum systems

  Kshitij Sharma, Himanshu Sahu, Subroto Mukerjee

  arXiv:2401.07215 · January 14, 2024 · quant-ph · SciPost Phys. 19, 120 (2025) · doi

  Abstract

  In this study, we explore the interplay between $\mathcal{PT}$-symmetry and quantum chaos in a non-Hermitian dynamical system. We consider an extension of the standard diagnostics of quantum chaos, namely the complex level spacing ratio and out-of-time-ordered correlators (OTOCs), to study the $\mathcal{PT}$-symmetric quantum kicked rotor model. The kicked rotor has long been regarded as a paradigmatic dynamic system to study classical and quantum chaos. By introducing non-Hermiticity in the quantum kicked rotor, we uncover new phases and transitions that are absent in the Hermitian system. From the study of the complex level spacing ratio, we locate three regimes -- one which is integrable and $\mathcal{PT}$-symmetry, another which is chaotic with $\mathcal{PT}$-symmetry and a third which is chaotic but with broken $\mathcal{PT}$-symmetry. We find that the complex level spacing ratio can distinguish between all three phases. Since calculations of the OTOC can be related to those of the classical Lyapunov exponent in the semi-classical limit, we investigate its nature in these regimes and at the phase boundaries. In the phases with $\mathcal{PT}$-symmetry, the OTOC exhibits behaviour akin to what is observed in the Hermitian system in both the integrable and chaotic regimes. Moreover, in the $\mathcal{PT}$-symmetry broken phase, the OTOC demonstrates additional exponential growth stemming from the complex nature of the eigenvalue spectrum at later times. We derive the analytical form of the late-time behaviour of the OTOC. By defining a normalized OTOC to mitigate the effects caused by $\mathcal{PT}$-symmetry breaking, we show that the OTOC exhibits singular behaviour at the transition from the $\mathcal{PT}$-symmetric chaotic phase to the $\mathcal{PT}$-symmetry broken, chaotic phase.

• Relativistic Quantum Fields Are Universal Entanglement Embezzlers

  Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, Henrik Wilming

  arXiv:2401.07292 · January 14, 2024 · quant-ph · Phys. Rev. Lett. 133, 261602 (2024) · doi

  Abstract

  Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system (the "embezzler") via local quantum operations while hardly perturbing the latter. We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras. Our result implies that relativistic quantum fields are universal embezzlers: Any entangled state of any dimension can be embezzled from them with arbitrary precision. This provides an operational characterization of the infinite amount of entanglement present in the vacuum state of relativistic quantum field theories.

• Generalized Quantum Stein's Lemma: Redeeming Second Law of Resource Theories

  Hayata Yamasaki, Kohdai Kuroiwa

  arXiv:2401.01926 · January 3, 2024 · quant-ph

  Abstract

  [Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brandão, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of [Bluhm, Capel, Gondolf, Pérez-Hernández, IEEE Trans. Inf. Theory 69, 5869 (2023)] used in our analysis. Due to this issue, the analysis in the previous version of this manuscript can no longer be considered complete proof of the generalized quantum Stein's lemma. This version is a temporal update to add this note. We are planning to update the manuscript further to explain the issue and what conditions we will additionally need to complete the proof of the generalized quantum Stein's lemma.]