Entanglement fluctuation theorems
Entanglement fluctuation theorems
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DOI：
10.1103/physreva.100.012317
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发表时间：
2017-09
影响因子：
2.9
通讯作者：
'Alvaro M. Alhambra;L. Masanes;J. Oppenheim;Christopher Perry
中科院分区：
文献类型：
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作者：
'Alvaro M. Alhambra;L. Masanes;J. Oppenheim;Christopher Perry
纯态纠缠变换被认为是不可逆的，可逆变换通常只在拷贝数的限制下才有可能。在这里，我们展示了可逆纠缠转换不需要在多副本级别上进行处理，而是可以在单个系统上进行，只要允许产生或消耗的纠缠量波动。在这种情况下，我们得到了纠缠操作的充分必要条件。作为推论，我们导出了一个量化纠缠涨落的方程，该方程与热力学中的Jarzynski涨落方程形式相同。我们也可以将正向纠缠转换与其反向过程联系起来，根据这种转换的纠缠成本，以一种相当于克鲁克斯关系的方式。我们证明了纠缠态变换的一个强逆定理与热力学第二定律有关，而纠缠态的施密特秩不能增加的事实与热力学第三定律有关。协议的实现是通过引入缠结电池来实现的，这种设备可以存储缠结并使用允许波动的缠结量，但平均成本仍然是最佳的。这让我们也解决了部分纠缠恢复的问题，事实上，我们证明了纠缠是完全恢复的。允许消耗的缠结量波动也会导致改进和最佳的缠结稀释方案。
Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.