Geometric optimization for quantum communication

• URL: http://arxiv.org/abs/2509.15106v2
• Date: Tue, 14 Oct 2025 15:32:47 GMT
• Title: Geometric optimization for quantum communication
• Authors: Chengkai Zhu, Hongyu Mao, Kun Fang, Xin Wang,
• Abstract summary: 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.
• Score: 9.522187892967727
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the phenomenon of superadditivity. This work develops Riemannian optimization methods to establish significantly tighter, computable two-sided bounds on these fundamental quantities. For upper bounds, our method systematically searches for state and channel extensions that minimize known information-theoretic bounds. We achieve this by parameterizing the space of all possible extensions as a Stiefel manifold, enabling a universal search that overcomes the limitations of ad-hoc constructions. Combined with an improved upper bound on the one-way distillable entanglement based on a refined continuity bound on quantum conditional entropy, our approach yields new state-of-the-art upper bounds on the quantum capacity of the qubit depolarizing channel for large values of the depolarizing parameter, strictly improving the previously best-known bounds. For lower bounds, we introduce Riemannian optimization methods to compute multi-shot coherent information. We establish lower bounds on the one-way distillable entanglement by parameterizing quantum instruments on the unitary manifold, and on the quantum capacity by parameterizing code states with a product of unitary manifolds. Numerical results for noisy entangled states and different channels demonstrate that our methods successfully unlock superadditive gains, improving previous results. Together, these findings establish Riemannian optimization as a principled and powerful tool for navigating the complex landscape of quantum communication limits. Furthermore, we prove that amortization does not enhance the channel coherent information, thereby closing a potential avenue for improving capacity lower bounds in general.

Related papers

• 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)
• Quartic quantum speedups for community detection [84.14713515477784]
  We develop a quantum algorithm for hypergraph community detection that achieves a quartic quantum speedup.<n>Our algorithm is based on the Kikuchi method, which we extend beyond previously considered problems such as PCA and $p$XORSAT.
  arXiv  Detail & Related papers  (2025-10-09T17:35:17Z)
• 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)
• Induced Quantum Divergence: A New Lens on Communication and Source Coding [4.3512163406552]
  This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding.<n>Two key applications are considered: classical communication over quantum channels, and quantum state redistribution.<n>Results provide new insights into fundamental single-shot quantum information protocols.
  arXiv  Detail & Related papers  (2025-02-19T12:25:56Z)
• Semidefinite optimization of the quantum relative entropy of channels [3.9134031118910264]
  This paper introduces a method for calculating the quantum relative entropy of channels. It provides efficiently computable upper and lower bounds that sandwich the true value with any desired precision.
  arXiv  Detail & Related papers  (2024-10-21T18:00:01Z)
• 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)
• Optimising the relative entropy under semidefinite constraints [0.0]
  Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem in quantum information theory.<n>We build on a recently introduced integral representation of quantum relative entropy by [Frenkel, Quantum 7, 1102 (2023) and provide reliable bounds as a sequence of semidefinite programs (SDPs)<n>Our approach ensures provable sublinear convergence in the discretization, while also maintaining resource efficiency in terms of SDP matrix dimensions.
  arXiv  Detail & Related papers  (2024-04-25T20:19:47Z)
• Computable and Faithful Lower Bound on Entanglement Cost [5.086696108576776]
  We develop computable and faithful lower bounds on the entanglement cost under quantum operations.<n>Our bounds are efficiently computable via semidefinite programming.<n>We extend our methodology to derive lower bounds on the entanglement cost of both point-to-point and bipartite quantum channels.
  arXiv  Detail & Related papers  (2023-11-17T17:07:26Z)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• 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)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• 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)

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.