论文标题
量子马尔可夫工艺的输出统计量的浓度不平等
Concentration Inequalities for Output Statistics of Quantum Markov Processes
论文作者
论文摘要
我们得出了新的浓度界限，以达到量子马尔可夫过程中测量结果的时间平均值。这概括了经典马尔可夫连锁店的众所周知的界限，这些界限为其平均值周围时间添加量的有限时间波动提供了限制。我们采用光谱，扰动和烈士技术，以及非交换性$ l_2 $理论来得出：（i）伯恩斯坦类型的浓度以量子马尔可夫链的测量结果平均为平均，（ii）hoeffding-type浓度的浓度连续的（iii）的连续性（iii）的概述（iii）的一般性计数，伯尔尼型的浓度是繁殖的。时间量子马尔可夫的过程，（iv）经典马尔可夫链的经验通量的新浓度界限扩大了相应的经验平均值以外的相应经典界限的适用性范围。我们还建议将结果的潜在应用到参数估计中，并考虑对还原量子通道，多时间统计和时间依赖性测量值进行扩展，并评论与所谓热力学不确定性关系的联系。
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive quantities around their averages. We employ spectral, perturbation and martingale techniques, together with noncommutative $L_2$ theory, to derive: (i) a Bernstein-type concentration bound for time averages of the measurement outcomes of a quantum Markov chain, (ii) a Hoeffding-type concentration bound for the same process, (iii) a generalization of the Bernstein-type concentration bound for counting processes of continuous time quantum Markov processes, (iv) new concentration bounds for empirical fluxes of classical Markov chains which broaden the range of applicability of the corresponding classical bounds beyond empirical averages. We also suggest potential application of our results to parameter estimation and consider extensions to reducible quantum channels, multi-time statistics and time-dependent measurements, and comment on the connection to so-called thermodynamic uncertainty relations.
