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Capacities of quantum Markovian noise for large times

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arxiv 2408.00116 v2 pith:DQEPUWLG submitted 2024-07-31 quant-ph math-phmath.MPmath.OA

Omar Fawzi , Mizanur Rahaman , Mostafa Taheri This is my paper
classification quant-phmath-phmath.MPmath.OA
keywords quantumcapacitiestimechannelclassicallargemarkoviannoise
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Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical and quantum capacities are characterized by efficiently computable properties of the peripheral spectrum of the quantum channel. In addition, the capacities are additive under tensor product, which implies in the language of Shannon theory that the one-shot and the asymptotic i.i.d. capacities are the same. We also provide an improved algorithm for computing the structure of the peripheral subspace of a quantum channel, which might be of independent interest.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Fixed points in de Finetti hierarchies

    quant-ph 2026-07 accept novelty 7.0 of 10

    Fixed-point constraints on de Finetti hierarchies yield O(√(log n)/n) double-sided rates, block-structured dimension dependence, and poly-time certifiable separable inner approximations for fixed local dimensions.

  2. Information transfer along the causal lightcone of a brickwork quantum circuit

    quant-ph 2026-05 unverdicted novelty 7.0 of 10

    Lossless information transfer along the causal lightcone in brickwork quantum circuits is enabled by peripheral eigenvalues of the M-qudit channel Φ_M, with examples for arbitrary N even in nonintegrable thermalising ...

  3. Fast convergence of Dynamic Capacities of GNS-Symmetric Quantum Channels

    quant-ph 2026-05 unverdicted novelty 5.0 of 10

    Explicit exponential convergence bounds are derived for the classical and quantum capacities of GNS-symmetric quantum channels in terms of entropic properties.

  4. Information storage and transmission under Markovian noise

    quant-ph 2025-04 unverdicted novelty 5.0 of 10

    Quantum Markov semigroups on d-dimensional systems have infinite-time capacities determined by peripheral space structure, with convergence after time t ≳ d² ln(d), and explicit bounds showing n-qubit memories fail af...

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