Papers

• Relative entropy of entanglement of Haar random states

  Takato Mori, Beni Yoshida

  arXiv:2608.05274 · August 5, 2026 · quant-ph

  Abstract

  We determine the relative entropy of entanglement of a bipartite mixed state $ρ_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|ψ\rangle_{ABC}$, finding $E_R(ρ_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(ρ_{AB})$ and the mutual information $I(A:B)$. The upper bound is achieved by an explicit separable state obtained through one-sided Schmidt dephasing, which is therefore approximately closest.

• Near-optimal quantum metrology with few-qubit measurements

  Liang Mao, Senrui Chen, Hsin-Yuan Huang, John Preskill, Sisi Zhou

  arXiv:2608.01617 · August 3, 2026 · quant-ph

  Abstract

  Quantum metrology, which addresses parameter estimation in quantum systems, has broad applications across science and technology. Conventional metrology protocols for multi-qubit states in the multi-parameter regime typically require highly complex quantum measurements, leading to substantial quantum-resource costs. In this work, we introduce a family of metrology protocols that use only few-qubit measurements, thereby significantly reducing the required resources. For arbitrary pure states, one of our protocols approaches the quantum Cramér-Rao bound up to an overhead in sample complexity that scales linearly with the number of qubits, irrespective of the number of parameters to be estimated. For typical Haar-random states, this overhead can be reduced to a constant. Our results build on recent advances in quantum state certification protocols with few-qubit measurements: we establish a universal connection between certification and metrology in which the precision of the certification protocol determines the metrological overhead. We also illustrate our approach through an example of Hamiltonian estimation from ground states.

• Counterexamples to additivity of minimum output $p$-Rényi entropy of quantum channels for $p>3/4$ and $0\leq p<1/4$

  Debbie Leung, Benjamin Lovitz, Peixue Wu

  arXiv:2607.15210 · July 16, 2026 · quant-ph

  Abstract

  Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and near $p=0$, while most of the interval $0<p<1$ has remained open. We prove that for every Rényi order $p$ satisfying either $p>3/4$ or $0\leq p<1/4$, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output $p$-Rényi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for $p>3/4$, and a transpose-complement rank-defect witness for $p<1/4$. Thus the unresolved part of $0<p<1$ is reduced to $[1/4,3/4]$. Our estimates also improve the output dimension threshold for additivity violation of minimum output von Neumann entropy, first established in Belinschi, Collins and Nechida.

• Efficient quantum algorithm for Heisenberg spin systems

  Sergey Bravyi, David Gosset, Yinchen Liu, Benjamin Wong

  arXiv:2607.14401 · July 15, 2026 · quant-ph

  Abstract

  We consider a broad family of Heisenberg-type quantum spin systems that were studied by Suzuki and Fisher in 1971. This family includes, for example, the Heisenberg antiferromagnet on any bipartite graph. The ground and Gibbs states of these models are Lee-Yang tensors with radius 1: they are associated with multilinear polynomials that possess an extraordinary zero-freeness property inside the unit polydisk in the complex plane. For each Hamiltonian in this family we show that the spectral gap between the first-excited and ground-state energies is lower bounded by $2μ$, where $μ$ is the magnetic field along the $Z$ direction. Using this result we obtain an efficient quantum adiabatic algorithm for the ground energy of any model in this family. The proof is based on a new inequality that relates the spectral gap of a positive semidefinite operator to its Lee-Yang radius -- a quantitative strengthening of prior work of the authors that may find applications elsewhere.

• Subregion observer rules from generalized entanglement wedges

  Lana Bozanic, Kenneth Higginbotham, Chris Waddell

  arXiv:2606.28484 · June 26, 2026 · hep-th

  Abstract

  We consider rules for modifying holographic tensor networks proposed in two independent contexts: by the Colorado (CO) group in 2503.09681 to incorporate observers in holographic maps, and by Kaya-Rath-Ritchie (KRR) in 2506.10064 to derive the Bousso-Penington generalized entanglement wedge proposal. Interestingly, these two sets of tensor network rules are exactly equivalent. This suggests a more general connection between these Abdalla-Antonini-Iliesiu-Levine (AAIL) inspired observer rules and generalized entanglement wedges. To pursue this connection, we first use KRR's analogous rules for the gravitational path integral (based on fixed geometry states) to generalize AAIL's path integral rules to include observers occupying a bulk subregion. Additionally, we leverage the connection in the opposite direction by using the AAIL rules to derive the Bousso-Penington proposal for pointlike bulk regions in JT gravity.

• Quantum-Limited Subdiffraction Telescopy Requires Genuine Multi-Telescope Interference

  Yujie Zhang, Yunkai Wang, Wilson Wu, Thomas Jennewein

  arXiv:2606.27276 · June 25, 2026 · quant-ph

  Abstract

  Conventional stellar interferometry reconstructs incoherent sources from pairwise mutual coherences between telescopes. Are such pairwise measurements sufficient for quantum-limited subdiffraction imaging with a telescope array? We show that for generic image-moment estimation, they are not. We consider weak incoherent light from a generic extended source observed by an array of telescopes, each supporting a single optical mode. For an N-telescope array, we derive the quantum Fisher information (QFI) scaling of image moments up to the cutoff 2N-2 and prove that arbitrary measurements restricted to telescope pairs attain the full-array QFI scaling only up to second order. Thus, estimating higher-order moments at the quantum limit requires genuinely multi-telescope interference. Inspired by spatial-mode demultiplexing (SPADE) from single-aperture subdiffraction imaging, we construct array-SPADE measurements that attain the optimal QFI scaling up to the finite-array cutoff. Finally, we show that these measurements can, in principle, be embedded in ancilla- and memory-assisted quantum-network architectures for long-baseline telescopy.

• Equivalence of non-local computation tasks beyond Clifford operations

  Andreas Bluhm, Simon Höfer, Alex May, Florian Speelman, Philip Verduyn Lunel

  arXiv:2606.26354 · June 24, 2026 · quant-ph

  Abstract

  Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglement. NLQC has applications in diverse areas, ranging from quantum position-verification to quantum gravity. Recently, it has been realized that the relationships among families of NLQC tasks are highly structured: many seemingly distinct tasks are related by reductions, wherein implementations of one task can be used to efficiently implement a second task. This is analogous to the notion of reduction in complexity theory, and reveals the relative hardness of NLQC tasks. In this work we continue the study of reductions among NLQC tasks. We focus on NLQC examples of the greatest interest in quantum position-verification; in particular examples involving large classical inputs and fixed-size quantum inputs, since these constitute the most feasible protocols for position-verification schemes. Within this setting, we find many new relationships among NLQC tasks. For instance, protocols for the simplest example of redirecting a quantum system based on a classical control imply protocols for controlled single qubit measurements in arbitrary bases, the controlled application of any Clifford unitary, and even the controlled application of any unitary of the form $U=C_1DC_0$ with $D$ an arbitrary diagonal unitary and $C_0, C_1$ Clifford circuits. This implies that many feasible position-verification schemes have the same asymptotic scaling for their entanglement cost, and hence a similar level of security. Our techniques rely on ideas from gate teleportation and measurement based quantum computation, among other areas, bringing several new strategies into NLQC which may be of independent interest.

• Many-body chirality of topological stabilizer states

  Tyler D. Ellison, Dongjin Lee, Zhi Li, Amin Moharramipour, Yasamin Panahi, Beni Yoshida

  arXiv:2606.20472 · June 18, 2026 · quant-ph

  Abstract

  A defining feature of chirality is the distinction between a system and its mirror image. Despite extensive experimental observations of chiral phases and theoretical advances, a quantum-information theoretic characterization of chirality based solely on the entanglement structure of many-body quantum states remains elusive. Here, we introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate through finite-depth local operations. We rigorously establish many-body chirality for stabilizer realizations of $\mathbb{Z}_d^{(k)}$ anyon theories, proving that complex conjugation can be implemented by local quantum channels if and only if the underlying anyon data are mirror invariant. This reveals forms of chirality that evade conventional diagnostics, including examples with vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations. We further show that this obstruction is intrinsically four-partite, while invisible to tripartite entanglement structure. Finally, we prove that $\mathbb{Z}_d^{(k)}$ states with $d>2$ possess intrinsic many-body imaginarity: their complex phase structure cannot be removed by finite-depth local unitaries. Remarkably, this includes states that are not many-body chiral.

• Subsystem Quantum Error Correction for Noisy Quantum Metrology

  Qiushi Liu, Sisi Zhou

  arXiv:2606.19628 · June 17, 2026 · quant-ph

  Abstract

  Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.

• Optimal classical shadow estimation of unitary channels at Heisenberg limit

  Entong He, Zihao Li, Noam Scully, Sisi Zhou, Yuxiang Yang

  arXiv:2606.13638 · June 11, 2026 · quant-ph

  Abstract

  Full tomography of an unknown quantum evolution is resource-intensive and often unnecessary when the goal is only to predict selected properties. This motivates the study of classical shadow estimation of unitary channels (CSEU), a task in which one queries an unknown $d$-dimensional unitary $U$ and stores classical data that can later be used to predict expectation values $\mathrm{tr}[O \cdot UρU^\dagger]$ up to additive error $\varepsilon$ for arbitrary input states $ρ$ and observables $O$. We propose a parallel, non-adaptive CSEU protocol using $\mathcal{O}(d\varepsilon^{-1})$ queries when the input states or observables have constant rank. This achieves Heisenberg scaling with respect to $\varepsilon$ and is query-optimal, as we prove a matching $Ω(d\varepsilon^{-1})$ lower bound that remains valid even with stronger access to the unknown unitary. Our query-optimal CSEU protocol provides a versatile and powerful tool for quantum learning theory, pushing the performance limits of several fundamental learning tasks, including unitary channel tomography, Hamiltonian learning, boundary-regime quantum channel tomography, Pauli transfer matrix learning, inverse-free amplitude estimation, pure-state property estimation, and shallow-circuit learning. Remarkably, we show that optimal unitary channel tomography can be achieved using only parallel queries, closing the gap between the best achievable efficiency of parallel and sequential tomography protocols. Together, these applications establish our framework as a fundamental tool for learning properties of quantum processes, particularly for certain key tasks that require high precision.

• New bounds on private simultaneous quantum message passing

  Uma Girish, Alex May, Natalie Parham, Henry Yuen

  arXiv:2606.12557 · June 10, 2026 · quant-ph

  Abstract

  In the private simultaneous message (PSM) setting, $k$ players obtain inputs $x_i\in\{0,1\}^n$ and then each send messages to a referee, who should learn $f(x_1,...,x_k)$ but no other information about $(x_1,...,x_k)$. The PSM setting was introduced as a minimal model for secure multiparty computation and has connections to Boolean function complexity. In the quantum setting, PSM has been related to non-local quantum computation (NLQC). The communication and correlation cost of implementing PSM remains poorly understood. Here, we give new upper and lower bounds on the (quantum) PSM model. For lower bounds, we show: 1) Nečiporuk's measure lower bounds the entanglement required for $k$-player quantum PSM with perfect correctness. This leads to quadratic lower bounds for explicit functions. 2) The rank of the communication matrix of $f(x_1,x_2)$ lower bounds 2-player quantum PSM with perfect privacy but imperfect correctness. This implies a previously unknown lower bound on classical PSM with imperfect correctness. When allowing quantum communication and shared entanglement, these are the first lower bounds on quantum PSM that make use of the privacy condition. For upper bounds, we show: 1) Letting $s$ be the size of a quantum circuit computing $f$, $d_f$ be the circuit depth, $k$ the number of players, $n$ the number of bits received by each player, and $ε$ a correctness parameter, we obtain $\mathsf{PSM}_k^*(f) \leq (kn +s) \cdot \log^{O(d_f)}(s/ε)$. 2) The square of the Fourier 1 norm of $f$, $\Vert \hat{f}\Vert_1^2$, upper bounds the classical PSM complexity, $\mathsf{PSM}(f)\leq O(\Vert \hat{f} \Vert^2_1)$. In proving the first upper bound, we generalize existing $T$-depth based techniques for NLQC from $2$ to $k\geq 2$ parties, and consider cases where the Clifford layers are restricted to having small light cones.

• Additivity Results for the Rényi-2 Entanglement of Purification

  Shokoufe Faraji, Zahra Baghali Khanian

  arXiv:2605.15439 · May 14, 2026 · quant-ph

  Abstract

  We reformulate the Rényi entanglement of purification as a constrained minimum output Rényi entropy problem. Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More precisely, for a completely positive map $Ω:L(B')\to L(A)$, we consider the quantity $\upsilon_p(Ω)$ defined by optimizing $\|(Ω\otimes \mathrm{id}_E)(σ^{B'E})\|_p$ over all bipartite states $σ^{B'E}$ whose $B'$-marginal is maximally mixed. We focus on the case $p=2$. First, we compute $\upsilon_2$ for the transpose-depolarizing channel and prove that it is multiplicative under tensor powers. We then establish a general multiplicativity criterion: whenever a completely positive map $N:L(B')\to L(A)$ satisfies $N^{\dagger} \mathbin{\circ} N=a\,\mathrm{id}_A+b\,\mathrm{Tr}[\cdot]\,I_d$ for some constants $a,b\ge 0$, where $N^{\dagger}$ denotes the Hilbert-Schmidt adjoint of $N$, the quantity $\upsilon_2(N)$ is multiplicative under tensor powers. Examples of channels satisfying this criterion include the transpose-depolarizing channel, the depolarizing channel, and their respective complementary channels. Furthermore, we show that, for every completely positive map $Ω$, multiplicativity of $\upsilon_p(Ω)$ implies multiplicativity for its complementary map. This yields the corresponding additivity statements for the associated Rényi-2 entanglement of purification.

• Distributed estimation of many-body Hamiltonians via punctured surface code

  Linmu Qiao, Zhichun Ouyang, Sisi Zhou

  arXiv:2605.11092 · May 11, 2026 · quant-ph

  Abstract

  We study how a punctured surface code can turn many local $Z$-type couplings into one protected logical signal for distributed quantum metrology, where the goal is to estimate a weighted average of the coupling strengths. We consider an ordinary planar patch with two $X$-cut holes and provide a distributed sensing protocol where all $Z$-type couplings correspond to the same nontrivial logical $\bar{Z}$ for the punctured surface code. When the couplings are disjoint, we show that the relevant global condition is equivalent to the existence of a closed dual loop, called a witness, that has an odd number of intersections with every chain. Together with a local clean opening condition, this witness criterion gives a concrete punctured-code construction in which all signal chains implement the same nontrivial logical $\bar Z$. For three-body interactions with overlapping supports, we also identify the class of interactions where our punctured surface code protocol applies. Overall, our results provide a novel, noise-robust distributed sensing protocol for many-body interactions, with corresponding topological design criteria.

• Graph-State Circuit Blocks control Entanglement and Scrambling Velocities

  Chandana Rao, Himanshu Sahu, Aranya Bhattacharya, Suhail Ahmad Rather, Mario Flory, Zahra Raissi

  arXiv:2605.11076 · May 11, 2026 · quant-ph

  Abstract

  Random circuit models often describe local dynamics using generic two-qubit gates, which have proven successful in capturing entanglement growth and operator spreading in many contexts. This approach naturally leads to the expectation that detailed gate structure plays only a limited role in coarse-grained entanglement and scrambling diagnostics. We show that the internal structure of multipartite circuit primitives can significantly influence these dynamical rates, even within a fixed random-circuit architecture. To investigate this, we study an exactly simulable family of Clifford quantum circuits built from fixed $n$-qubit graph-state preparation unitaries, which we treat as elementary building blocks. Specifically, we consider a one-dimensional chain of $N$ qubits initialized in a product state and evolved by layers in which nonoverlapping length-$n$ blocks are placed at uniformly random positions with sparsity $α$. We find that different choices of graph-state building blocks lead to strongly varying dynamical rates. Graph states that are inequivalent under local Clifford (LC) transformations generate sharply different entanglement velocities $v_E$ and butterfly velocities $v_B$, even though the circuits are drawn from the same ensemble with identical architecture and randomness parameters. We further show that this hierarchy is captured by two complementary block-level characteristics: the distribution of entanglement across internal bipartitions of the graph state, which correlates with $v_E$, and a graph-theoretic connectivity profile across bipartitions, which correlates with $v_B$. Neither descriptor alone fully determines the dynamics; rather, entanglement growth and operator spreading are controlled by distinct structural features of the local circuit blocks. Notably, AME states appear among the fastest scrambling building blocks within the ensembles studied here.

• Enhanced quantum capacity thresholds from symmetry

  Avantika Agarwal, Amolak Ratan Kalra, Sungjai Lee, Debbie Leung, Luke Schaeffer, Pulkit Sinha, Graeme Smith

  arXiv:2605.09138 · May 9, 2026 · quant-ph

  Abstract

  The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

• Quantum metrology via partial quantum error correction

  Yinan Chen, Zongyuan Wang, Sisi Zhou

  arXiv:2605.08341 · May 8, 2026 · quant-ph

  Abstract

  We introduce a method for error-corrected quantum metrology where only partial quantum error correction (QEC) is needed to suppress local noise and maintain the probe states' super-standard-quantum-limit (super-SQL) sensing performance. This stands in contrast to the existing QEC-assisted sensing schemes in Phys. Rev. Lett. 112, 080801 (2014) and Phys. Rev. Lett. 112, 150802 (2014), where a probe state is encoded into the logical subspace of a quantum code and error correction involves measurements on all checks of the code. Here, we encode the probe states into superpositions of energetically different states of the underlying quantum code. For our probe states, error correction using a subset of checks is enough to suppress noise both before and after phase imprinting. We analyze the tradeoff in noise suppression. For noise parallel to our phase imprinter of weight $l$, we achieve a suppression of $p^δ$ where $p$ is the noise strength and $δ= \lfloor (l+1)/2 \rfloor$. We propose an adaptive imprinter weight increasing strategy to maintain super-SQL performance as we scale up the system. In all our examples, checks and phase imprinters are chosen to be local operators avoiding non-local connectivity.

• Quantum metrology of mixed states via purification

  Sisi Zhou

  arXiv:2605.03975 · May 5, 2026 · quant-ph

  Abstract

  We introduce new formulations of the quantum Cramér-Rao bound (QCRB) and the Holevo Cramér-Rao bound (HCRB) in multi-parameter quantum metrology via purification, where we show their values for any mixed state are connected to that for its purification with nuisance parameters introduced on the environmental system. Using this technique, we develop a new method for asymptotically attaining either the HCRB or twice the QCRB for arbitrary mixed states using random purification channels and individual measurements.

• Entanglement cost in non-local quantum computation

  Alex May

  arXiv:2605.02840 · May 4, 2026 · quant-ph

  Abstract

  This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.

• A Unified Framework for Locally Stable Phases

  Zhi Li, Raz Firanko, Timothy H. Hsieh

  arXiv:2605.00088 · April 30, 2026 · quant-ph

  Abstract

  We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short range correlated, defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of a family of nonlinear correlators, including the fidelity correlator, and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable (short range correlated) states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.

• Sufficiency and Petz recovery for positive maps

  Lauritz van Luijk, Henrik Wilming

  arXiv:2604.08380 · April 9, 2026 · quant-ph

  Abstract

  We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of minimal sufficient Jordan algebras, which can be seen to generalize the Koashi-Imoto decomposition to the PTP setting. In particular, we show that Neyman-Pearson tests generate the minimal sufficient Jordan algebra, and hence also the minimal sufficient *-algebra corresponding to the Koashi-Imoto decomposition. As applications, we show that a) equality in the data-processing inequality for the relative entropy or the $α$-$z$ quantum Rényi divergence implies the existence of a recovery map also in the PTP case and b) that two dichotomies can be interconverted by PTP maps if and only if they can be interconverted by decomposable, trace-preserving maps. We thoroughly review the necessary mathematical background on Jordan algebras. As a step beyond the finite-dimensional case, we prove Frenkel's formula for approximately finite-dimensional von Neumann algebras.

• On Error Thresholds for Pauli Channels: Some answers with many more questions

  Avantika Agarwal, Alan Bu, Amolak Ratan Kalra, Debbie Leung, Luke Schaeffer, Graeme Smith

  arXiv:2603.04357 · March 4, 2026 · quant-ph

  Abstract

  This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we study potential non-additivity of a variety of small stabilizer codes and their concatenations, and report several new concatenated stabilizer codes of small length that show significant non-additivity. We also give a closed form expression of coset weight enumerators of concatenated phase and bit flip repetition codes. Using insights from this formalism, we estimate the threshold for concatenated repetition codes of large lengths. Finally, for several concatenations of small stabilizer codes we optimize for channels which lead to maximal non-additivity at the hashing point of the corresponding channel. We supplement these results with a discussion on the performance of various stabilizer codes from the perspective of the non-additivity and threshold problem. We report both positive and negative results, and highlight some counterintuitive observations, to support subsequent work on lower bounds for error thresholds.

• Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach

  Senrui Chen, Weiyuan Gong, Sisi Zhou

  arXiv:2602.04952 · February 4, 2026 · quant-ph · Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:1115-1185, 2026

  Abstract

  We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $ρ$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to estimate expectation values $\{\mathrm{tr}(O_iρ)\}_{i=1}^m$ to accuracy $ε$ in $L_p$-norm, using possibly adaptive measurements that act on $O(\mathrm{polylog}(d))$ number of copies of $ρ$ at a time. We focus on the regime where $ε$ is below an instance-dependent threshold. Our main contribution is an instance-optimal characterization of the sample complexity as $\tildeΘ(Γ_p/ε^2)$, where $Γ_p$ is a function of $\{O_i\}_{i=1}^m$ defined via an optimization formula involving the inverse Fisher information matrix. Previously, tight bounds were known only in special cases, e.g. Pauli shadow tomography with $L_\infty$-norm error. Concretely, we first analyze a simpler oblivious variant where the goal is to estimate an observable of the form $\sum_{i=1}^m α_i O_i$ with $\|α\|_q = 1$ (where $q$ is dual to $p$) revealed after the measurement. For single-copy measurements, we obtain a sample complexity of $Θ(Γ^{\mathrm{ob}}_p/ε^2)$. We then show $\tildeΘ(Γ_p/ε^2)$ is necessary and sufficient for the original problem, with the lower bound applying to unbiased, bounded estimators. Our upper bounds rely on a two-step algorithm combining coarse tomography with local estimation. Notably, $Γ^{\mathrm{ob}}_\infty = Γ_\infty$. In both cases, allowing $c$-copy measurements improves the sample complexity by at most $Ω(1/c)$. Our results establish a quantitative correspondence between quantum learning and metrology, unifying asymptotic metrological limits with finite-sample learning guarantees.

• Lee-Yang tensors and Hamiltonian complexity

  Benjamin Wong, Sergey Bravyi, David Gosset, Yinchen Liu

  arXiv:2602.03605 · February 3, 2026 · quant-ph

  Abstract

  A complex tensor with $n$ binary indices can be identified with a multilinear polynomial in $n$ complex variables. We say it is a Lee-Yang tensor with radius $r$ if the polynomial is nonzero whenever all variables lie in the open disk of radius $r$. In this work we study quantum states and observables which are Lee-Yang tensors when expressed in the computational basis. We first review their basic properties, including closure under tensor contraction and certain quantum operations. We show that quantum states with Lee-Yang radius $r > 1$ can be prepared by quasipolynomial-sized circuits. We also show that every Hermitian operator with Lee-Yang radius $r > 1$ has a unique principal eigenvector. These results suggest that $r = 1$ is a key threshold for quantum states and observables. Finally, we consider a family of two-local Hamiltonians where every interaction term energetically favors a deformed EPR state $|00\rangle + s|11\rangle$ for some $0 \leq s \leq 1$. We numerically investigate this model and find that on all graphs considered the Lee-Yang radius of the ground state is at least $r = 1/\sqrt{s}$ while the spectral gap between the two smallest eigenvalues is at least $1-s^2$. We conjecture that these lower bounds hold more generally; in particular, this would provide an efficient quantum adiabatic algorithm for the quantum Max-Cut problem on uniformly weighted bipartite graphs.

• Lower bounds on non-local computation from controllable correlation

  Richard Cleve, Alex May

  arXiv:2602.00255 · January 30, 2026 · quant-ph

  Abstract

  Understanding entanglement cost in non-local quantum computation (NLQC) is relevant to complexity, cryptography, gravity, and other areas. This entanglement cost is largely uncharacterized; previous lower bound techniques apply to narrowly defined cases, and proving lower bounds on most simple unitaries has remained open. Here, we give two new lower bound techniques that can be evaluated for any unitary, based on their controllable correlation and controllable entanglement. For Haar random two qubit unitaries, our techniques typically lead to non-trivial lower bounds. Further, we obtain lower bounds on most of the commonly studied two qubit quantum gates, including CNOT, DCNOT, $\sqrt{\text{SWAP}}$, and the XX interaction, none of which previously had known lower bounds. For the CNOT gate, one of our techniques gives a tight lower bound, fully resolving its entanglement cost. The resulting lower bounds have parallel repetition properties, and apply in the noisy setting.

• Accelerating De Novo Genome Assembly via Quantum-Assisted Graph Optimization with Bitstring Recovery

  Jaya Vasavi Pamidimukkala, Himanshu Sahu, Ashwini Kannan, Janani Ananthanarayanan, Kalyan Dasgupta, Sanjib Senapati

  arXiv:2602.00156 · January 29, 2026 · quant-ph

  Abstract

  Genome sequencing is essential to decode genetic information, identify organisms, understand diseases and advance personalized medicine. A critical step in any genome sequencing technique is genome assembly. However, de novo genome assembly, which involves constructing an entire genome sequence from scratch without a reference genome, presents significant challenges due to its high computational complexity, affecting both time and accuracy. In this study, we propose a hybrid approach utilizing a quantum computing-based optimization algorithm integrated with classical pre-processing to expedite the genome assembly process. Specifically, we present a method to solve the Hamiltonian and Eulerian paths within the genome assembly graph using gate-based quantum computing through a Higher-Order Binary Optimization (HOBO) formulation with the Variational Quantum Eigensolver algorithm (VQE), in addition to a novel bitstring recovery mechanism to improve optimizer traversal of the solution space. A comparative analysis with classical optimization techniques was performed to assess the effectiveness of our quantum-based approach in genome assembly. The results indicate that, as quantum hardware continues to evolve and noise levels diminish, our formulation holds a significant potential to accelerate genome sequencing by offering faster and more accurate solutions to the complex challenges in genomic research.

• Efficient learning of logical noise from syndrome data

  Han Zheng, Chia-Tung Chu, Senrui Chen, Argyris Giannisis Manes, Su-un Lee, Sisi Zhou, Liang Jiang

  arXiv:2601.22286 · January 29, 2026 · quant-ph

  Abstract

  Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabilities are suppressed to higher order relative to physical noise and are therefore difficult to calibrate through direct logical measurements. Recently, Wagner et al. [PRL 130, 200601 (2023)] showed that, for phenomenological Pauli noise models, the logical channel can instead be inferred from syndrome measurement data generated during error correction. Here, we extend this framework to realistic circuit-level noise models. From a unified code-theoretic perspective and spacetime code formalism, we derive necessary and sufficient conditions for learning the logical channel from syndrome data alone and explicitly characterize the learnable degrees of freedom of circuit-level Pauli faults. Using Fourier analysis and compressed sensing, we develop efficient estimators with provable guarantees on sample complexity and computational cost. We further present an end-to-end protocol and demonstrate its performance on several syndrome-extraction circuits, achieving orders-of-magnitude sample-complexity savings over direct logical benchmarking. Our results establish syndrome-based learning as a practical approach to characterizing the logical channel in fault-tolerant quantum devices.

• Entanglement summoning from entanglement sharing

  Lana Bozanic, Alex May, Stanley Miao

  arXiv:2601.15112 · January 21, 2026 · quant-ph

  Abstract

  In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.

• Achieving the Heisenberg limit using fault-tolerant quantum error correction

  Himanshu Sahu, Qian Xu, Sisi Zhou

  arXiv:2601.05457 · January 9, 2026 · quant-ph

  Abstract

  Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum error correction (QEC) can recover the HL in various scenarios. A notable example is estimating a Pauli-$Z$ signal under bit-flip noise using the repetition code, which is both optimal for metrology and robust against noise. However, previous protocols often assume noise affects only the signal accumulation step, while the QEC operations -- including state preparation and measurement -- are noiseless. To overcome this limitation, we study fault-tolerant quantum metrology where all qubit operations are subject to noise. We focus on estimating a Pauli-$Z$ signal under bit-flip noise, together with state preparation and measurement errors in all QEC operations. We propose a fault-tolerant metrological protocol where a repetition code is prepared via repeated syndrome measurements, followed by a fault-tolerant logical measurement. We demonstrate the existence of an error threshold, below which errors are effectively suppressed and the HL is attained.

• Gradient descent reliably finds depth- and gate-optimal circuits for generic unitaries

  Janani Gomathi, Alex Meiburg

  arXiv:2601.03123 · January 6, 2026 · quant-ph

  Abstract

  When the gate set has continuous parameters, synthesizing a unitary operator as a quantum circuit is always possible using exact methods, but finding minimal circuits efficiently remains a challenging problem. The landscape is very different for compiled unitaries, which arise from programming and typically have short circuits, as compared with generic unitaries, which use all parameters and typically require circuits of maximal size. We show that simple gradient descent reliably finds depth- and gate-optimal circuits for generic unitaries, including in the presence of restricted chip connectivity. This runs counter to earlier evidence that optimal synthesis required combinatorial search, and we show that this discrepancy can be explained by avoiding the random selection of certain parameter-deficient circuit skeletons.