Enhanced quantum capacity thresholds from symmetry

• URL: http://arxiv.org/abs/2605.09138v2
• Date: Wed, 13 May 2026 17:21:15 GMT
• Title: Enhanced quantum capacity thresholds from symmetry
• Abstract summary: We show significant increases in capacity thresholds of two prototypical noise models.<n>In the case of the depolarizing channel, this is the first improvement in 18 years.<n>A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space.
• Score: 2.8241852537721353
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Asymptotic Limits of Entanglement Distribution [43.748379918040854]
  We investigate the limits of entanglement distribution across quantum networks utilizing intermediate stations and local operations.<n>We establish a strict dichotomy: the preservation of entanglement over arbitrarily long distances is possible if the underlying quantum channel admits a correctable subspace.<n>We derive a fundamental lower bound on the physical resource requirements, proving that for channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement.
  arXiv  Detail & Related papers  (2026-05-22T09:56:38Z)
• Quantum-Channel Matrix Optimization for Holevo Bound Enhancement [87.57725685513088]
  We propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble.<n> Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.
  arXiv  Detail & Related papers  (2026-02-19T04:15:03Z)
• Fundamental Quality Bound on Optical Quantum Communication [16.94403919812334]
  We prove that entanglement's entropy sharpens the rate of distillation under non-entangling operations.<n>These findings offer a new perspective on entanglement as a resource for future quantum optical networks.
  arXiv  Detail & Related papers  (2025-10-08T15:12:37Z)
• Geometric optimization for quantum communication [9.522187892967727]
  We study the limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state.<n>For upper bounds, our method searches for state and channel extensions that minimize known information-theoretic bounds.<n>For lower bounds, we establish lower bounds on the one-way distillable entanglement by parameterizing quantum instruments on the unitary manifold.
  arXiv  Detail & Related papers  (2025-09-18T16:13:07Z)
• Improving quantum communication rates with permutation-invariant codes [6.107978190324034]
  We improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes.<n>For each channel family we obtain improved lower bounds on their quantum capacities.
  arXiv  Detail & Related papers  (2025-08-13T17:47:51Z)
• Optimizing entanglement distribution via noisy quantum channels [44.99833362998488]
  Entanglement distribution is a crucial problem in quantum information science.<n>We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels.
  arXiv  Detail & Related papers  (2025-06-06T13:48:20Z)
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes.<n>Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Entanglement catalysis for quantum states and noisy channels [41.94295877935867]
  We investigate properties of entanglement and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel.
  arXiv  Detail & Related papers  (2022-02-10T18:36:25Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Maximum Relative Entropy of Coherence for Quantum Channels [0.6685158490869523]
  We introduce a new coherence quantifier for quantum channels via maximum relative entropy. We show that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations.
  arXiv  Detail & Related papers  (2021-06-30T15:03:01Z)
• Creating and destroying coherence with quantum channels [62.997667081978825]
  We study optimal ways to create a large amount of quantum coherence via quantum channels. correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We show that a channel can destroy more coherence when acting on a subsystem of a bipartite state.
  arXiv  Detail & Related papers  (2021-05-25T16:44:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.