Total versus quantum correlations in quantum states
Total versus quantum correlations in quantum states
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DOI：
10.1103/physreva.76.032327
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发表时间：
2007-09
影响因子：
2.9
通讯作者：
Nan Li;S. Luo
中科院分区：
文献类型：
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作者：
Nan Li;S. Luo
在二分量子态中的总相关性由量子互信息测量，并且将总相关性分离为量子部分和经典部分满足直观的支配关系的前提下，我们研究了各种熵纠缠度量，例如可蒸馏纠缠，相对熵纠缠，压扁纠缠，纠缠成本和形成纠缠，在多大程度上可以被视为 量子相关性的一致测量。我们说明，形成的纠缠常常高估了量子相关性，因此太大而无法真正衡量量子相关性。这表明形成的纠缠并不能量化量子态固有的量子相关性，而是表征通过局部操作和经典通信构建量子态所需的纯纠缠。此外，它的结论是，如果形成纠缠的加性猜想为真（正如人们广泛认为的那样），那么纠缠成本（一种操作上定义的具有重要物理意义的纠缠度量）不能是量子相关性的一致度量，因为它可能超过总相关性。或者，如果纠缠成本由总相关性主导，正如我们的直觉所表明的那样，那么我们可以立即反驳加性猜想。这两种情况都有其违反直觉和吸引人的方面，在这种情况下出现的一个自然挑战是证明或反驳纠缠成本由量子互信息主导。
On the premises that total correlations in a bipartite quantum state are measured by the quantum mutual information, and that separation of total correlations into quantum and classical parts satisfies an intuitive dominance relation, we examine to what extent various entropic entanglement measures, such as the distillable entanglement, the relative entropy entanglement, the squashed entanglement, the entanglement cost, and the entanglement of formation, can be regarded as consistent measures of quantum correlations. We illustrate that the entanglement of formation often overestimates quantum correlations and thus is too big to be a genuine measure of quantum correlations. This indicates that the entanglement of formation does not quantify the quantum correlations intrinsic to a quantum state, but rather characterizes the pure entanglement needed to build the quantum state via local operations and classical communication. Furthermore, it has the consequence that, if the additive conjecture for the entanglement of formation is true (as is widely believed), then the entanglement cost, which is an operationally defined measure of entanglement with significant physical meaning, cannot be a consistent measure of quantum correlations in the sense that it may exceed total correlations. Alternatively, if the entanglement cost is dominated by total correlations, as our intuition suggests, then we can immediately disprove the additive conjecture. Both scenarios have their counterintuitive and appealing aspects, and a natural challenge arising in this context is to prove or disprove that the entanglement cost is dominated by the quantum mutual information.