Capacities of quantum Markovian noise for large times

Omar Fawzi, Mizanur Rahaman, Mostafa Taheri
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Abstract

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.
量子马尔可夫噪声的大时间能力
给定一个量子马尔可夫噪声模型,我们研究了可以存储任意大时间的经典或量子系统的最大维度。我们发现,与固定时间的设置不同,在无限时间的极限中,经典容量和量子容量的特征是量子通道外围频谱的可有效计算特性。此外,容量在张量乘积下是相加的,这意味着用香农理论的语言来说,单次容量和渐近 i.i.d. 容量是相同的。我们还提供了一种计算量子信道外围子空间结构的改进算法,这可能会引起人们的兴趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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