Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
复制标题
DOI：
10.1103/prxquantum.3.020318
复制
发表时间：
2021-12
期刊：
影响因子：
9.7
通讯作者：
Arshag Danageozian;M. Wilde;F. Buscemi
中科院分区：
文献类型：
--
作者：
Arshag Danageozian;M. Wilde;F. Buscemi
量子纠错（QEC）是一个程序，通过该程序，系统的量子态被保护免受已知类型的噪声，通过抢先添加冗余到该状态。当存在热噪声时，这种过程通常用于量子计算。有趣的是，热噪声也被认为在量子热力学（QTD）中发挥着核心作用。这一事实暗示了某些QTD陈述在热噪声QEC中的适用性，这在之前的麦克斯韦恶魔的背景下已经讨论过。在本文中，我们将QEC视为具有反馈控制器的量子热机（即，恶魔）。我们推导出的误差识别阶段的Groenewold信息增益的测量过程中耗散的热量的上限，从而提供了后者的物理意义，也当它是负的。此外，我们推导出热力学第二定律的背景下，这个QEC引擎，操作与一般的量子测量。最后，我们表明，根据一组物理动机的假设，这导致一个基本的三重权衡关系，这意味着之间的权衡QEC的最大可实现的保真度和超卡诺效率的热机与反馈控制器已被称为拥有。对于QEC引擎的热力学效率和用于错误识别的量子测量的功效，发生类似的权衡关系。
Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is commonly used in quantum computing when thermal noise is present. Interestingly, thermal noise has also been known to play a central role in quantum thermodynamics (QTD). This fact hints at the applicability of certain QTD statements in the QEC of thermal noise, which has been discussed previously in the context of Maxwell's demon. In this article, we view QEC as a quantum heat engine with a feedback controller (i.e., a demon). We derive an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain, thereby providing the latter with a physical meaning also when it is negative. Further, we derive the second law of thermodynamics in the context of this QEC engine, operating with general quantum measurements. Finally, we show that, under a set of physically motivated assumptions, this leads to a fundamental triple trade-off relation, which implies a trade-off between the maximum achievable fidelity of QEC and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess. A similar trade-off relation occurs for the thermodynamic efficiency of the QEC engine and the efficacy of the quantum measurement used for error identification.