Papers 2025

• Helping observers in closed universes reach their full potential

  Kenneth Higginbotham

  arXiv:2512.17993 · December 19, 2025 · hep-th

  Abstract

  Recent work by Engelhardt, Gesteau, and Harlow applies proposals for incorporating observers into holographic maps to study the Antonini-Rath puzzle for closed universes. In a new form of ``observer complementarity,'' they find that an AdS bulk observer measures a SWAP test to determine that there is no closed universe in the bulk, contrary to the (limited) description given by an observer inside the closed universe. In this work, we improve the predictions of both observers by using the holographic maps to define new operators to perform this same SWAP test. With these, we show that the AdS observer cannot rule out a baby universe in the bulk, and the closed universe observer can improve the accuracy of their description.

• Baby universe as logical qubits: information recovery in random encoding

  Takato Mori, Beni Yoshida

  arXiv:2511.20747 · November 25, 2025 · hep-th

  Abstract

  We revisit whether a semiclassical closed baby universe in AdS/CFT necessarily possess a trivial one-dimensional Hilbert space or may instead carry a large entropy. Recent results on Haar random encoding suggest a breakdown of complementary recovery, in which no logical operators can be reconstructed from individual bipartite subsystems. Motivated by this, we propose an interpretation where a baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, assuming pseudorandom dynamics in holographic CFT correlators. We then analyze two conceptual puzzles: an apparent cloning of baby-universe microstates and its eventual fate at the singularity. Both puzzles are avoided because no single boundary observer can access the baby-universe degrees of freedom, be it classical or quantum, reflecting an emergent form of complementarity due to the structure of random encoding. In this interpretation, observers arise naturally: the same heavy operator that prepares the baby-universe geometry also serves as observer-like degrees of freedom that define an observer-dependent baby-universe microstate.

• Inherently unpredictable beam steering for quantum LiDAR

  Junyeop Kim, Dongjin Lee, Woncheol Shin, Yeoulheon Seong, Heedeuk Shin

  arXiv:2511.09089 · November 12, 2025 · quant-ph · doi

  Abstract

  Quantum LiDAR offers noise resilience and stealth observation capabilities in low-light conditions. In prior demonstrations, the telescope pointing was raster-scanned, making the observation direction predictable from the pointing direction. However, while Quantum LiDAR can enable stealth observation, operational stealth is enhanced by inherently unpredictable beam steering. Here, we introduce a novel stealth beam steering method that is fundamentally immune to prediction. In a photon pair, the probe photon undergoes diffraction in an unpredictable direction at a grating due to wavelength randomness. The arrival time of the heralding photon, delayed by propagation through a dispersive medium, enables the determination of the probe photon's diffraction direction. Our method successfully detects multiple targets in parallel, demonstrating up to a 1000-fold enhancement in signal-to-noise ratio compared to classical LiDAR. This breakthrough establishes a new paradigm for quantum-enhanced sensing, with far-reaching implications for quantum metrology, secure communications, and beyond.

• Self-Configuring Quantum Networks with Superposition of Trajectories

  Albie Chan, Zheng Shi, Jorge Miguel-Ramiro, Luca Dellantonio, Christine A. Muschik, Wolfgang Dür

  arXiv:2510.19092 · October 21, 2025 · quant-ph

  Abstract

  Quantum networks are a backbone of future quantum technologies thanks to their role in communication and scalable quantum computing. However, their performance is challenged by noise and decoherence. We propose a self-configuring approach that integrates superposed quantum paths with variational quantum optimization techniques. This allows networks to dynamically optimize the superposition of noisy paths across multiple nodes to establish high-fidelity connections between different parties. Our framework is in principle capable of adapting to unknown noise without requiring detailed characterization or benchmarking of the corresponding quantum channels. We also discuss the role of vacuum coherence, a quantum effect central to path superposition that impacts protocol performance. Additionally, we demonstrate that our approach remains beneficial even in the presence of imperfections in the generation of path superposition.

• Buildings for Synthesis with Clifford+R

  Mark Deaconu, Nihar Gargava, Amolak Ratan Kalra, Michele Mosca, Jon Yard

  arXiv:2510.11526 · October 13, 2025 · quant-ph

  Abstract

  We study the problem of exact synthesis for the Clifford+R gate set and give the explicit structure of the underlying Bruhat-Tits building for this group. In this process, we also give an alternative proof of the arithmetic nature of this gate set.

• A Formalization of the Generalized Quantum Stein's Lemma in Lean

  Alex Meiburg, Leonardo A. Lessa, Rodolfo R. Soldati

  arXiv:2510.08672 · October 9, 2025 · quant-ph

  Abstract

  The Generalized Quantum Stein's Lemma is a theorem in quantum hypothesis testing that provides an operational meaning to the relative entropy within the context of quantum resource theories. Its original proof was found to have a gap, which led to a search for a corrected proof. We formalize the proof presented in [Hayashi and Yamasaki (2024)] in the Lean interactive theorem prover. This is the most technically demanding theorem in physics with a computer-verified proof to date, building with a variety of intermediate results from topology, analysis, and operator algebra. In the process, we rectified minor imprecisions in [HY24]'s proof that formalization forces us to confront, and refine a more precise definition of quantum resource theory. Formalizing this theorem has ensured that our Lean-QuantumInfo library, which otherwise has begun to encompass a variety of topics from quantum information, includes a robust foundation suitable for a larger collaborative program of formalizing quantum theory more broadly.

• The charge-singlet measurement toolbox

  Abhijit Chakraborty, Randy Lewis, Christine A. Muschik

  arXiv:2510.08718 · October 9, 2025 · quant-ph

  Abstract

  Symmetry is fundamental to physical laws across different scales$—$from spacetime structure in general relativity to particle interactions in quantum field theory. Local symmetries, described by gauge theories, are central to phenomena such as superconductivity, topological phases, and the Standard Model of particle physics. Emerging simulation techniques using tensor network states or quantum computers offer exciting new possibilities of exploring the physics of these gauge theories, but require careful implementation of gauge symmetry and charge-neutrality constraints. This is especially challenging for non-Abelian gauge theories such as quantum chromodynamics (QCD), which governs the strong interaction between quarks and gluons. In a recent article (arXiv:2501.00579), we introduced "charge-singlet measurements" for quantum simulations, consisting of a projection based technique from group representation theory that allowed us to probe for the first time the phase diagram of (1+1)-dimensional QCD on a quantum computer. In this article, we show more broadly how to apply charge-singlet measurements as a flexible tool for both classical and quantum simulations of discrete and continuous gauge theories. Our approach extends the use of charge-singlet measurements beyond state preparation in the charge neutral (charge-singlet) sector to include noise mitigation in symmetry-preserving time-evolution circuits. We further demonstrate how this method enables the computation of thermodynamic observables$—$such as entropy$—$within the charge-singlet subspace, providing a new tool for exploring the connection between quantum thermodynamics and gauge symmetry.

• Entanglement in von Neumann Algebraic Quantum Information Theory

  Lauritz van Luijk

  arXiv:2510.07563 · October 8, 2025 · quant-ph · PhD thesis, Leibniz University Hanover, 2025 · doi

  Abstract

  In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entanglement in such systems, we use a framework in which subsystems are described by von Neumann algebras on the full system's Hilbert space. Although this approach has been known for over 50 years, an operational justification has been missing so far. We resolve this by deriving the von Neumann algebraic description of subsystems from operational axioms. This raises the question of how physical properties of the subsystem relate to algebraic properties. Our main result shows a surprisingly strong connection: The type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in one-to-one correspondence with a family of operational entanglement properties. For instance, Connes' classification of type III factors can be formulated in terms of the smallest achievable error when "embezzling" entanglement from the system. Our findings promote the type classification from algebraic bookkeeping to a classification of infinite quantum systems based on the kind of infinite entanglement that they support.

• Magic and communication complexity

  Uma Girish, Alex May, Natalie Parham, Henry Yuen

  arXiv:2510.07246 · October 8, 2025 · quant-ph

  Abstract

  We establish novel connections between magic in quantum circuits and communication complexity. In particular, we show that functions computable with low magic have low communication cost. Our first result shows that the $\mathsf{D}\|$ (deterministic simultaneous message passing) cost of a Boolean function $f$ is at most the number of single-qubit magic gates in a quantum circuit computing $f$ with any quantum advice state. If we allow mid-circuit measurements and adaptive circuits, we obtain an upper bound on the two-way communication complexity of $f$ in terms of the magic + measurement cost of the circuit for $f$. As an application, we obtain magic-count lower bounds of $Ω(n)$ for the $n$-qubit generalized Toffoli gate as well as the $n$-qubit quantum multiplexer. Our second result gives a general method to transform $\mathsf{Q}\|^*$ protocols (simultaneous quantum messages with shared entanglement) into $\mathsf{R}\|^*$ protocols (simultaneous classical messages with shared entanglement) which incurs only a polynomial blowup in the communication and entanglement complexity, provided the referee's action in the $\mathsf{Q}\|^*$ protocol is implementable in constant $T$-depth. The resulting $\mathsf{R}\|^*$ protocols satisfy strong privacy constraints and are $\mathsf{PSM}^*$ protocols (private simultaneous message passing with shared entanglement), where the referee learns almost nothing about the inputs other than the function value. As an application, we demonstrate $n$-bit partial Boolean functions whose $\mathsf{R}\|^*$ complexity is $\mathrm{polylog}(n)$ and whose $\mathsf{R}$ (interactive randomized) complexity is $n^{Ω(1)}$, establishing the first exponential separations between $\mathsf{R}\|^*$ and $\mathsf{R}$ for Boolean functions.

• Multi-qubit Toffoli with exponentially fewer T gates

  David Gosset, Robin Kothari, Chenyi Zhang

  arXiv:2510.07223 · October 8, 2025 · quant-ph

  Abstract

  Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a tiny $1/\mathrm{poly}(n)$ error that can be neglected in most practical situations. More precisely, the $n$-qubit Toffoli gate can be implemented to within error $ε$ in the diamond distance by a randomly chosen Clifford+$T$ circuit with at most $O(\log(1/ε))$ $T$ gates. We also give a matching $Ω(\log(1/ε))$ lower bound that establishes optimality, and we show that any purely unitary implementation achieving even constant error must use $Ω(n)$ $T$ gates. We also extend our sampling technique to implement other Boolean functions. Finally, we describe upper and lower bounds on the $T$-count of Boolean functions in terms of non-adaptive parity decision tree complexity and its randomized analogue.

• Quantum capacity amplification via privacy

  Peixue Wu, Yunkai Wang

  arXiv:2510.04527 · October 6, 2025 · quant-ph

  Abstract

  We investigate superadditivity of quantum capacity through private channels whose Choi-Jamiolkowski operators are private states. This perspective links the security structure of private states to quantum capacity and clarifies the role of the shield system: information encoded in the shield system that would otherwise leak to the environment can be recycled when paired with an assisting channel, thereby boosting capacity. Our main contributions are threefold: Firstly, we develop a general framework that provides a sufficient condition for capacity amplification, which is formulated in terms of the assisting channel's Holevo information. As examples, we give explicit, dimension and parameter dependent amplification thresholds for erasure and depolarizing channels. Secondly, assuming the Spin alignment conjecture, we derive a single-letter expression for the quantum capacity of a family of private channels that are neither degradable, anti-degradable, nor PPT; as an application, we construct channels with vanishing quantum capacity yet unbounded private capacity. Thirdly, we further analyze approximate private channels: we give an alternative proof of superactivation that extends its validity to a broader parameter regime, and, by combining amplification bounds with continuity estimates, we establish a metric separation showing that channels exhibiting capacity amplification have nonzero diamond distance from the set of anti-degradable channels, indicating that existing approximate (anti-)degradability bounds are not tight. We also revisit the computability of the regularized quantum capacity and modestly suggest that this fundamental question still remains open.

• Optimizing fermionic Hamiltonians with classical interactions

  Maarten Stroeks, Barbara M. Terhal, Yaroslav Herasymenko

  arXiv:2510.02122 · October 2, 2025 · quant-ph

  Abstract

  We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a fundamental fact that underpins electronic-structure Hamiltonians in quantum chemistry and condensed matter. We prove that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for such Hamiltonians, independent of sparsity. This shows that classical interactions are sufficient to prevent the vanishing Gaussian approximation ratio observed in SYK-type models. We also give efficient semi-definite programming algorithms for Gaussian approximations to several families of traceless and positive-semidefinite classically interacting Hamiltonians, with the ability to enforce a fixed particle number. The technical core of our results is the concept of a Gaussian blend, a construction for Gaussian states via mixtures of covariance matrices.

• On sufficient conditions for holographic scattering

  Caroline Lima, Sabrina Pasterski, Chris Waddell

  arXiv:2509.26264 · September 30, 2025 · hep-th

  Abstract

  Holography implies scattering in the bulk can be mediated by entanglement on the boundary. The connected wedge theorem (CWT) of May, Penington, and Sorce is a concrete example where bulk scattering implies correlation between certain boundary regions. However the converse does not hold. We investigate a recent proposal of Leutheusser and Liu for a generalization of the CWT with converse. We prove the forward direction: having pairs of CFT ``input'' (and likewise ``output'') regions in a phase with connected entanglement wedge implies that a particular bulk subregion (the intersection of ``input'' and ``output'' entanglement wedges) is non-empty. We then establish a modified version of the proposal which has a converse, and identify counter-examples to the stronger conjecture.

• Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark

  Minhui Zhu, Minyang Tian, Xiaocheng Yang, Tianci Zhou, Lifan Yuan, Penghao Zhu, Eli Chertkov, Shengyan Liu, Yufeng Du, Ziming Ji … Yunkai Wang … et al.

  arXiv:2509.26574 · September 30, 2025 · cs.AI

  Abstract

  While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And crucially, what kinds of reasoning tasks do physicists want LLMs to assist with? To address these questions, we present the CritPt (Complex Research using Integrated Thinking - Physics Test, pronounced "critical point"), the first benchmark designed to test LLMs on unpublished, research-level reasoning tasks that broadly covers modern physics research areas, including condensed matter, quantum physics, atomic, molecular & optical physics, astrophysics, high energy physics, mathematical physics, statistical physics, nuclear physics, nonlinear dynamics, fluid dynamics and biophysics. CritPt consists of 71 composite research challenges designed to simulate full-scale research projects at the entry level, which are also decomposed to 190 simpler checkpoint tasks for more fine-grained insights. All problems are newly created by 50+ active physics researchers based on their own research. Every problem is hand-curated to admit a guess-resistant and machine-verifiable answer and is evaluated by an automated grading pipeline heavily customized for advanced physics-specific output formats. We find that while current state-of-the-art LLMs show early promise on isolated checkpoints, they remain far from being able to reliably solve full research-scale challenges: the best average accuracy among base models is only 5.7%, achieved by GPT-5 (high), moderately rising to around 10% when equipped with coding tools. Through the realistic yet standardized evaluation offered by CritPt, we highlight a large disconnect between current model capabilities and realistic physics research demands, offering a foundation to guide the development of scientifically grounded AI tools.

• Entanglement sharing schemes

  Zahra Khanian, Dongjin Lee, Debbie Leung, Zhi Li, Alex May, Takato Mori, Stanley Miao, Farzin Salek, Jinmin Yi, Beni Yoshida

  arXiv:2509.21462 · September 25, 2025 · quant-ph

  Abstract

  We ask how quantum correlations can be distributed among many subsystems. To address this, we define entanglement sharing schemes (ESS) where certain pairs of subsystems allow entanglement to be recovered via local operations, while other pairs must not. ESS schemes come in two variants, one where the partner system with which entanglement should be prepared is known, and one where it is not. In the case of known partners, we fully characterize the access structures realizable for ESS when using stabilizer states, and construct efficient schemes for threshold access structures, and give a conjecture for the access structures realizable with general states. In the unknown partner case, we again give a complete characterization in the stabilizer setting, additionally give a complete characterization of the case where there are no restrictions on unauthorized pairs, and we prove a set of necessary conditions on general schemes which we conjecture are also sufficient. Finally, we give an application of the theory of entanglement sharing to resolve an open problem related to the distribution of entanglement in response to time-sensitive requests in quantum networks.

• Chiral Color Code : Single-shot error correction for exotic topological order

  Dongjin Lee, Beni Yoshida

  arXiv:2509.18324 · September 22, 2025 · quant-ph

  Abstract

  We present a family of simple three-dimensional stabilizer codes, called the chiral color codes, that realize fermionic and chiral topological orders. In the qubit case, the code realizes the topological phase of a single copy of the fermionic toric code. For qudit systems with local dimension $d$, the model features a chiral parameter $α$ and realizes 3D topological phases characterized by $\mathbb{Z}_d^{(α)}$ anyon theories with anomalous chiral surface topological order. On closed manifolds, the code has a unique ground state after removing bulk transparent fermions or bosons. Furthermore, we prove that the bulk is short-range entangled (for odd $d$, coprime $α$) by constructing an explicit local quantum channel that prepares the ground state. The chiral color codes are constructed within the gauge color code, and hence inherit its fault-tolerant features: they admit single-shot error correction and allow code switching to other stabilizer color codes. These properties position the chiral color codes as particularly useful platforms for realizing and manipulating fermions and chiral anyons.

• Gaussian fermionic embezzlement of entanglement

  Alessia Kera, Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2509.15749 · September 19, 2025 · quant-ph

  Abstract

  Embezzlement of entanglement allows to extract arbitrary entangled states from a suitable embezzling state using only local operations while perturbing the resource state arbitrarily little. A natural family of embezzling states is given by ground states of non-interacting, critical fermions in one spatial dimension. This raises the question of whether the embezzlement operations can be restricted to Gaussian operations whenever one only wishes to extract Gaussian entangled states. We show that this is indeed the case and prove that the embezzling property is in fact a generic property of fermionic Gaussian states. Our results provide a fine-grained understanding of embezzlement of entanglement for fermionic Gaussian states in the finite-size regime and thereby bridge finite-size systems to abstract characterizations based on the classification of von Neumann algebras. To prove our results, we establish novel bounds relating the distance of covariances to the trace-distance of Gaussian states, which may be of independent interest.

• Uniqueness of purifications is equivalent to Haag duality

  Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2509.12911 · September 16, 2025 · quant-ph · doi

  Abstract

  The uniqueness of purifications of quantum states on a system $A$ up to local unitary transformations on a purifying system $B$ is central to quantum information theory. We show that, if the two systems are modelled by commuting von Neumann algebras $M_A$ and $M_B$ on a Hilbert space $\mathcal H$, then uniqueness of purifications is equivalent to Haag duality $M_A = M_B'$. In particular, the uniqueness of purifications can fail in systems with infinitely many degrees of freedom -- even when $M_A$ and $M_B$ are commuting factors that jointly generate $B(\mathcal H)$ and hence allow for local tomography of all density matrices on $\mathcal H$.

• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits

  Sarah Meng Li, Michele Mosca, Neil J. Ross, John van de Wetering, Yuming Zhao

  arXiv:2508.14670 · August 20, 2025 · cs.LO · EPTCS 426, 2025, pp. 23-78 · doi

  Abstract

  We present a complete set of rewrite rules for n-qutrit Clifford circuits where n is any non-negative integer. This is the first completeness result for any fragment of quantum circuits in odd prime dimensions. We first generalize Selinger's normal form for n-qubit Clifford circuits to the qutrit setting. Then, we present a rewrite system by which any Clifford circuit can be reduced to this normal form. We then simplify the rewrite rules in this procedure to a small natural set of rules, giving a clean presentation of the group of qutrit Clifford unitaries in terms of generators and relations.

• Revisiting the operator extension of strong subadditivity

  Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2508.03731 · July 30, 2025 · math.OA

  Abstract

  We give a new proof of the operator extension of the strong subadditivity of von Neumann entropy $ρ_{AB} \otimes σ_{C}^{-1} \leq ρ_{A} \otimes σ_{BC}^{-1}$ by identifying the mathematical structure behind it as Connes' theory of spatial derivatives. This immediately generalizes the inequality to arbitrary inclusions of von Neumann algebras. In the case of standard representations, it reduces to the monotonicity of the relative modular operator.

• On Strong Converse Bounds for the Private and Quantum Capacities of Anti-degradable Channels

  Zahra Baghali Khanian, Christoph Hirche

  arXiv:2507.15661 · July 21, 2025 · quant-ph

  Abstract

  We establish a strong converse bound for the private classical capacity of anti-degradable quantum channels. Specifically, we prove that this capacity is zero whenever the error $ε> 0$ and privacy parameter $δ> 0$ satisfy the inequality $δ(1-ε^2)^{\frac{1}{2}}+ε(1-δ^2)^{\frac{1}{2}}<1$. This result strengthens previous understandings by sharply defining the boundary beyond which reliable and private communication is impossible. Furthermore, we present a ``pretty simple'' proof of the ``pretty strong'' converse for the quantum capacity of anti-degradable channels, valid for any error $ε< \frac{1}{\sqrt{2}}$. Our approach offers clarity and technical simplicity, shedding new light on the fundamental limits of quantum communication.

• On tests for baby universes in AdS/CFT

  Kenneth Higginbotham

  arXiv:2507.05337 · July 7, 2025 · hep-th

  Abstract

  To address a puzzle by Antonini and Rath -- where a single CFT state has two bulk duals, one with a baby universe and one without -- Engelhardt and Gesteau recently devised a test for baby universes in AdS/CFT. Using the extrapolate dictionary, they showed that the boundary dual of a bulk swap test favored bulk spacetimes without a baby universe, providing evidence against their semiclassical validity. However, recent work suggests that holographic maps should post-select on such closed universes, and we argue that this is consistent with the extrapolate dictionary. We therefore construct a new holographic map for bulk states with baby universes and use this to show that the swap test cannot distinguish between Antonini and Rath's two candidate bulk duals. This not only allows for a valid semiclassical description of the baby universe, but also enables the application of recent techniques for including observers in holographic maps.

• Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes

  Ricardo Rivera Cardoso, Alex Meiburg, Daniel Nagaj

  arXiv:2506.07244 · June 8, 2025 · quant-ph

  Abstract

  Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\mathsf{P}$; or complete for $\mathsf{NP}$, $\mathsf{MA}$, or $\mathsf{QMA_1}$. Here, we demonstrate new qubit variants of this problem that are complete for $\mathsf{BQP_1}$, $\mathsf{coRP}$, $\mathsf{QCMA}$, $\mathsf{PI(coRP,NP)}$, $\mathsf{PI(BQP_1,NP)}$, $\mathsf{PI(BQP_1,MA)}$, $\mathsf{SoPU(coRP,NP)}$, $\mathsf{SoPU(BQP_1,NP)}$, and $\mathsf{SoPU(BQP_1,MA)}$. Our result implies that a complete classification of quantum constraint satisfaction problems (QCSPs), analogous to Schaefer's dichotomy theorem for classical CSPs, must either include these 13 classes, or otherwise show that some are equal. Additionally, our result showcases two new types of QSAT problems that can be decided efficiently, as well as the first nontrivial $\mathsf{BQP_1}$-complete problem. We first prove there are qudit QSAT problems that are complete for $\mathsf{BQP_1}$, $\mathsf{coRP}$, and $\mathsf{QCMA}$ by re-defining elements of the circuit-to-Hamiltonian transformation. We then show that any QCSP can be reduced to a problem in qubits while maintaining the same complexity - something believed not to be possible classically. The remaining six problems are obtained by considering "sums" and "products" of the first seven QSAT problems. Before this work, the QSAT problems generated in this way resulted in complete problems for $\mathsf{PI}$ and $\mathsf{SoPU}$ classes that were trivially equal to other known classes. We thus commence the study of these new and seemingly nontrivial classes. While [Meiburg, 2021] first sought to prove completeness for the first three classes, we note that his constructions are flawed. Here, we rework them and obtain improvements on the required qudit dimensionality.

• A complexity theory for non-local quantum computation

  Andreas Bluhm, Simon Höfer, Alex May, Mikka Stasiuk, Philip Verduyn Lunel, Henry Yuen

  arXiv:2505.23893 · May 29, 2025 · quant-ph · Quantum 10, 2152 (2026) · doi

  Abstract

  Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a characterization of entanglement cost in at least certain NLQC tasks would imply significant breakthroughs in complexity theory. Here, we avoid these obstructions and take an indirect approach to understanding resource requirements in NLQC, which mimics the approach used by complexity theorists: we study the relative hardness of different NLQC tasks by identifying resource efficient reductions between them. Most significantly, we prove that $f$-measure and $f$-route, the two best studied NLQC tasks, are in fact equivalent under $O(1)$ overhead reductions. This result simplifies many existing proofs in the literature and extends several new properties to $f$-measure. For instance, we obtain sub-exponential upper bounds on $f$-measure for all functions, and efficient protocols for functions in the complexity class $\mathsf{Mod}_k\mathsf{L}$. Beyond this, we study a number of other examples of NLQC tasks and their relationships.

• Suggestions of decreasing dark energy from supernova and BAO data: an update

  Mark Van Raamsdonk, Chris Waddell

  arXiv:2505.10662 · May 15, 2025 · astro-ph.CO

  Abstract

  In a previous work 2305.04946, we found that supernova and baryon acoustic oscillation data support the hypothesis that late time cosmic acceleration is caused by the potential energy of a scalar field descending its potential, as suggested by holographically defined models of quantum gravity. In this note, we update our analysis using the Dark Energy Survey 5 year supernova data set (DES-SN5YR) and the baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2). Approximating the scalar potential via a first order Taylor series $V \approx V_0 + V_1 φ$ about the present value, and making use of only recent-time data from DES-SN5YR and DESI DR2, we find that the slope parameter is constrained as $V_1 = 1.49 \pm 0.25$ in a standard likelihood analysis. This is naively a $>5 σ$ discrepancy with $Λ$CDM (which has $V_1 =0$), though a more detailed analysis not assuming a Gaussian likelihood distribution suggests $4 σ$ significance. Based only on the $Δχ^2 = -13.7$ improvement of fit while ignoring parameter space volumes disfavours $Λ$CDM at a $3 σ$ significance level. These significance measures are substantially improved from our previous analysis using older data sets. We also reproduce the DESI DR2 parameter constraints based on the same combination of data and find that the $Λ$CDM is more strongly disfavoured in the context of the linear potential extension (dubbed $V_0V_1$) as compared with the $w_0 w_a$ extension of $Λ$CDM. A caveat is that for both $w_0 w_a$ and $V_0 V_1$, much of the significance relies on the historical $z < 0.1$ supernova samples included in the DES-SN5YR data set.

• Efficiently Computable Limits on EPR Pair Generation in Quantum Broadcast Channels

  Patrick Hayden, Debbie Leung, Hjalmar Rall, Farzin Salek

  arXiv:2505.07218 · May 12, 2025 · quant-ph

  Abstract

  We investigate the generation of EPR pairs between three observers in a general causally structured setting, where communication occurs via a noisy quantum broadcast channel. The most general quantum codes for this setup take the form of tripartite quantum channels. Since the receivers are constrained by causal ordering, additional temporal relationships naturally emerge between the parties. These causal constraints enforce intrinsic no-signalling conditions on any tripartite operation, ensuring that it constitutes a physically realizable quantum code for a quantum broadcast channel. We analyze these constraints and, more broadly, characterize the most general quantum codes for communication over such channels. We examine the capabilities of codes that are fully no-signalling among the three parties, positive partial transpose (PPT)-preserving, or both, and derive simple semidefinite programs to compute the achievable entanglement fidelity. We then establish a hierarchy of semidefinite programming converse bounds -- both weak and strong -- for the capacity of quantum broadcast channels for EPR pair generation, in both one-shot and asymptotic regimes. Notably, in the special case of a point-to-point channel, our strong converse bound recovers and strengthens existing results. Finally, we demonstrate how the PPT-preserving codes we develop can be leveraged to construct PPT-preserving entanglement combing schemes, and vice versa.

• Secure quantum ranging

  Yunkai Wang, Graeme Smith, Alex May

  arXiv:2505.04776 · May 7, 2025 · quant-ph

  Abstract

  Determining and verifying an object's position is a fundamental task with broad practical relevance. We propose a secure quantum ranging protocol that combines quantum ranging with quantum position verification (QPV). Our method achieves Heisenberg-limited precision in position estimation while simultaneously detecting potential cheaters. Two verifiers each send out a state that is entangled in frequency space within a single optical mode. An honest prover only needs to perform simple beam-splitter operations, whereas cheaters are allowed to use arbitrary linear optical operations, one ancillary mode, and perfect quantum memories-though without access to entanglement. Our approach considers a previously unstudied security aspect to quantum ranging. It also provides a framework to quantify the precision with which a prover's position can be verified in QPV, which previously has been assumed to be infinite.

• Comparing classical and quantum conditional disclosure of secrets

  Uma Girish, Alex May, Leo Orshansky, Chris Waddell

  arXiv:2505.02939 · May 5, 2025 · quant-ph · Quantum 10, 2049 (2026) · doi

  Abstract

  The conditional disclosure of secrets (CDS) setting is among the most basic primitives studied in information-theoretic cryptography. Motivated by a connection to non-local quantum computation and position-based cryptography, CDS with quantum resources has recently been considered. Here, we study the differences between quantum and classical CDS, with the aims of clarifying the power of quantum resources in information-theoretic cryptography. We establish the following results: 1) We prove a $Ω(\log \mathsf{R}_{0,A\rightarrow B}(f)+\log \mathsf{R}_{0,B\rightarrow A}(f))$ lower bound on quantum CDS where $\mathsf{R}_{0,A\rightarrow B}(f)$ is the classical one-way communication complexity with perfect correctness. 2) We prove a lower bound on quantum CDS in terms of two round, public coin, two-prover interactive proofs. 3) For perfectly correct CDS, we give a separation for a promise version of the not-equals function, showing a quantum upper bound of $O(\log n)$ and classical lower bound of $Ω(n)$. 4) We give a logarithmic upper bound for quantum CDS on forrelation, while the best known classical algorithm is linear. We interpret this as preliminary evidence that classical and quantum CDS are separated even with correctness and security error allowed. We also give a separation for classical and quantum private simultaneous message passing for a partial function, improving on an earlier relational separation. Our results use novel combinations of techniques from non-local quantum computation and communication complexity.

• Quantum Reverse Shannon Theorem Revisited

  Zahra Baghali Khanian, Debbie Leung

  arXiv:2504.07068 · April 9, 2025 · quant-ph

  Abstract

  Reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones. This is dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one. The Quantum Reverse Shannon Theorem is extensively studied by Bennett and co-authors in [IEEE Trans. Inf. Theory, 2014]. They present two distinct theorems, each tailored to classical and quantum channel simulations respectively, explaining the fact that these theorems remain incomparable due to the fundamentally different nature of correlations they address. The authors leave as an open question the challenge of formulating a unified theorem that could encompass the principles of both and unify them. We unify these two theorems into a single, comprehensive theorem, extending it to the most general case by considering correlations with a general mixed-state reference system. Furthermore, we unify feedback and non-feedback theorems by simulating a general side information system at the encoder side.

• Streaming quantum state purification for general mixed states

  Daniel Grier, Debbie Leung, Zhi Li, Hakop Pashayan, Luke Schaeffer

  arXiv:2503.22644 · March 28, 2025 · quant-ph

  Abstract

  Given multiple copies of a mixed quantum state with an unknown, nondegenerate principal eigenspace, quantum state purification is the task of recovering a quantum state that is closer to the principal eigenstate. A streaming protocol relying on recursive swap tests has been proposed and analysed for noisy depolarized states with arbitrary dimension and noise level. Here, we show that the same algorithm applies much more broadly, enabling the purification of arbitrary mixed states with a nondegenerate principal eigenvalue. We demonstrate this through two approaches. In the first approach, we show that, given the largest two eigenvalues, the depolarized noise is the most difficult noise to purify for the recursive swap tests, thus the desirable bounds on performance and cost follow from prior work. In the second approach, we provide a new and direct analysis for the performance of purification using recursive swap tests for the more general noise. We also derive simple lower bounds on the sample complexity, showing that the recursive swap test algorithm attains optimal sample complexity (up to a constant factor) in the low-noise regime.

• Fault-tolerant Preparation of Distant Logical Bell Pair -- with application in the magic square game

  Andy Zeyi Liu, Debbie Leung

  arXiv:2503.13673 · March 17, 2025 · quant-ph

  Abstract

  Measures of quantum nonlocality traditionally assume perfect local computation. In real experiments, however, each computational primitive is imperfect. Fault-tolerant techniques enable arbitrarily accurate quantum computation but do not necessarily preserve optimized measures of nonlocality. We examine the impact of low noise on quantum nonlocality in nonlocal games, where even small imperfections can disproportionately increase entanglement consumption. Focusing on the fault-tolerant magic square game, we optimize the tradeoff between noisy entanglement consumption and deficit in the game value. We introduce an interface circuit and logical entanglement purification protocol (EPP) to efficiently translate states between physical and logical qubits and purify noisy logical Bell pair, reducing Bell pair consumption. Our analytical and numerical results, particularly for the $[[7^k,1,3^k]]$ concatenated Steane code, demonstrate exponential Bell pair savings and a higher noise threshold. We establish theoretical lower bounds for local noise threshold of $4.70\times10^{-4}$ and an initial Bell pair infidelity threshold of $18.3\%$. Our framework is adaptable to various quantum error-correcting codes (QECCs) and experimental platforms. This work not only advances fault-tolerant nonlocal games but also inspires further research on interfacing different QECCs, fostering modular quantum architectures and the quantum internet.

• On observers in holographic maps

  Chris Akers, Gracemarie Bueller, Oliver DeWolfe, Kenneth Higginbotham, Johannes Reinking, Rudolph Rodriguez

  arXiv:2503.09681 · March 12, 2025 · hep-th

  Abstract

  A straightforward gravitational path integral calculation implies that closed universes are trivial, described by a one dimensional Hilbert space. Two recent papers by Harlow-Usatyuk-Zhao and Abdalla-Antonini-Iliesiu-Levine have sought to ameliorate this issue by defining special rules to incorporate observers into the path integral. However, the proposed rules are different, leading to differing results for the Hilbert space dimension. Moreover, the former work offers a holographic map realized using a non-isometric code construction to complement their path integral result and clarify its physics. In this work, we propose a non-isometric code that implements the second construction, allowing thorough comparison. Our prescription may be thought of as simply removing the portion of the map that acts on the observer, while preserving the rest, creating an effective holographic boundary at the observer-environment interface. This proposal can be directly applied to general holographic maps for both open and closed universes of any dimension.

• Quantum Error Corrected Non-Markovian Metrology

  Zachary Mann, Ningping Cao, Raymond Laflamme, Sisi Zhou

  arXiv:2503.07745 · March 10, 2025 · quant-ph · PRX Quantum 6, 030321 (2025) · doi

  Abstract

  Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL) - the fundamental precision bound set by quantum mechanics - is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the hidden Markov model and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

• Limitations of Gaussian measurements in quantum imaging

  Yunkai Wang, Sisi Zhou

  arXiv:2503.06363 · March 9, 2025 · quant-ph

  Abstract

  Imaging thermal sources naturally yields Gaussian states at the receiver, raising the question of whether Gaussian measurements can perform optimally in quantum imaging. In this work, we establish no-go theorems on the performance of Gaussian measurements for imaging thermal sources in the limit of mean photon number per temporal mode $ε\to 0$ or source size $L \to 0$. We show that non-Gaussian measurements can outperform any Gaussian measurement in the scaling of the estimation variance with $ε$ (or $L$). We also present several examples to illustrate the no-go results.

• The Large-Scale Structure of Entanglement in Quantum Many-body Systems

  Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming

  arXiv:2503.03833 · March 5, 2025 · quant-ph

  Abstract

  We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems -- similar to how phase transitions only sharply emerge in the thermodynamic limit. The resulting operational entanglement properties are in one-to-one correspondence with abstract properties of the local observable algebras that emerge in the thermodynamic limit. These properties are insensitive to finite perturbations and hence describe the $\textit{large-scale structure of entanglement}$ of many-body systems. We formulate and discuss the emerging structures and open questions, both for gapped and gapless many-body systems. In particular, we show that every gapped phase of matter, even the trivial one, in $D\geq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement. Conversely, we conjecture the existence of topological phases of matter, where all representatives have the strongest form of entanglement.

• Quantum learning advantage on a scalable photonic platform

  Zheng-Hao Liu, Romain Brunel, Emil E. B. Østergaard, Oscar Cordero, Senrui Chen, Yat Wong, Jens A. H. Nielsen, Axel B. Bregnsbo, Sisi Zhou, Hsin-Yuan Huang … et al.

  arXiv:2502.07770 · February 11, 2025 · quant-ph · Science 389, 1332--1335 (2025) · doi

  Abstract

  Recent advancements in quantum technologies have opened new horizons for exploring the physical world in ways once deemed impossible. Central to these breakthroughs is the concept of quantum advantage, where quantum systems outperform their classical counterparts in solving specific tasks. While much attention has been devoted to computational speedups, quantum advantage in learning physical systems remains a largely untapped frontier. Here, we present a photonic implementation of a quantum-enhanced protocol for learning the probability distribution of a multimode bosonic displacement process. By harnessing the unique properties of continuous-variable quantum entanglement, we obtain a massive advantage in sample complexity with respect to conventional methods without entangled resources. With approximately 5 dB of two-mode squeezing -- corresponding to imperfect Einstein--Podolsky--Rosen (EPR) entanglement -- we learn a 100-mode bosonic displacement process using 11.8 orders of magnitude fewer samples than a conventional scheme. Our results demonstrate that even with non-ideal, noisy entanglement, a significant quantum advantage can be realized in continuous-variable quantum systems. This marks an important step towards practical quantum-enhanced learning protocols with implications for quantum metrology, certification, and machine learning.

• Tripartite Haar random state has no bipartite entanglement

  Zhi Li, Takato Mori, Beni Yoshida

  arXiv:2502.04437 · February 6, 2025 · quant-ph

  Abstract

  We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitaries or local operations when each subsystem $A$, $B$, or $C$ has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net argument and concentration of measure. Viewing $|Ψ\rangle_{ABC}$ as a bipartite quantum error-correcting code $C\to AB$, this implies that neither output subsystem $A$ nor $B$ supports any non-trivial logical operator. We also establish general constraints on the structure of tripartite entanglement in Haar random states, showing that W- or GHZ-like entanglement cannot be distilled and that nontrivial global symmetries are absent. Finally, we discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement, contrary to a previous belief.

• Randomized measurements for multi-parameter quantum metrology

  Sisi Zhou, Senrui Chen

  arXiv:2502.03536 · February 5, 2025 · quant-ph · PRX Quantum 7, 010314 (2026) · doi

  Abstract

  The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the Holevo Cramér--Rao bound, suffer from multiple difficulties towards practical applicability, as the optimal measurement strategies are usually state-dependent, difficult to implement and also take complex analyses to determine. Here we study randomized measurements as a new approach for multi-parameter quantum metrology. We show quantum measurements on single copies of quantum states given by $3$-designs perform near-optimally when estimating an arbitrary number of parameters in pure states and more generally, {approximately low-rank well-conditioned states}, whose metrological information is largely concentrated in a low-dimensional subspace. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on their supports. Examples of fidelity estimation and Hamiltonian estimation are explicitly provided to demonstrate the power and limitation of randomized measurements in multi-parameter quantum metrology.

• Gaussian quantum data hiding

  Yunkai Wang, Graeme Smith

  arXiv:2502.00670 · February 2, 2025 · quant-ph

  Abstract

  Quantum data hiding encodes a hidden classical bit to a pair of quantum states that is difficult to distinguish using a particular set of measurement, denoted as $M$. In this work, we explore quantum data hiding in two contexts involving Gaussian operations or states. First, we consider the set of measurement $M$ as Gaussian local quantum operations and classical communication, a new set of operations not previously discussed in the literature for data hiding. We hide one classical bit in the two different mixture of displaced two-mode squeezed states. Second, we consider the set of measurement $M$ as general Gaussian measurement and construct the data hiding states using two-mode thermal states. This data hiding scheme is effective in the weak strength limit, providing a new example compared to existing discussions for the set of general Gaussian measurement.

• Advancing quantum imaging through learning theory

  Yunkai Wang, Changhun Oh, Junyu Liu, Liang Jiang, Sisi Zhou

  arXiv:2501.15685 · January 26, 2025 · quant-ph · Nature Comm. 17, 1124 (2026)

  Abstract

  We study quantum imaging by applying the resolvable expressive capacity (REC) formalism developed for physical neural networks (PNNs). In this paradigm of quantum learning, the imaging system functions as a physical learning device that maps input parameters to measurable features, while complex practical tasks are handled by training only the output weights, enabled by the systematic identification of well-estimated features (eigentasks) and their corresponding sample thresholds. Using this framework, we analyze both direct imaging and superresolution strategies for compact sources, defined as sources with sizes bounded below the Rayleigh limit. In particular, we introduce the orthogonalized SPADE method-a nontrivial generalization of existing superresolution techniques-that achieves superior performance when multiple compact sources are closely spaced. This method relaxes the earlier superresolution studies' strong assumption that the entire source must lie within the Rayleigh limit, marking an important step toward developing more general and practically applicable approaches. Using the example of face recognition, which involve complex structured sources, we demonstrate the superior performance of our orthogonalized SPADE method and highlight key advantages of the quantum learning approach-its ability to tackle complex imaging tasks and enhance performance by selectively extracting well-estimated features.

• Classical and quantum algorithms for characters of the symmetric group

  Sergey Bravyi, David Gosset, Vojtech Havlicek, Louis Schatzki

  arXiv:2501.12579 · January 22, 2025 · quant-ph

  Abstract

  Characters of irreducible representations are ubiquitous in group theory. However, computing characters of some groups such as the symmetric group $S_n$ is a challenging problem known to be $\#P$-hard in the worst case. Here we describe a Matrix Product State (MPS) algorithm for characters of $S_n$. The algorithm computes an MPS encoding all irreducible characters of a given permutation. It relies on a mapping from characters of $S_n$ to quantum spin chains proposed by Crichigno and Prakash. We also provide a simpler derivation of this mapping. We complement this result by presenting a $poly(n)$ size quantum circuit that prepares the corresponding MPS, obtaining an efficient quantum algorithm for certain sampling problems based on characters of $S_n$. To assess classical hardness of these problems we present a general reduction from strong simulation (computing a given probability) to weak simulation (sampling with a small error). This reduction applies to any sampling problem with a certain granularity structure and may be of independent interest.