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arXiv quant-ph/0410090quant-ph
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量子信息理论中的定域与非定域信息：形式与现象

Local versus non-local information in quantum information theory: formalism and phenomena

Michal Horodecki, Pawel Horodecki, Ryszard Horodecki, Jonathan Oppenheim, Aditi Sen De, Ujjwal Sen, Barbara Synak

备注：
35 pages in two column, 4 figures
发表信息：
Phys. Rev. A 71, 062307 (2005)
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摘要：

尽管在量子信息理论中有许多结果，但复合系统的复杂性远未被清楚。一般来说，信息是本地和非本地（“量子”）信息的混合。为了使这一点更清楚，我们开发和研究的量子信息处理范式中，各方共享一个多体状态提取本地信息。由于各方必须使用传统的通信渠道而丢失的信息量是赤字。这个方案可以被看作是对提取纠缠概念的补充。在回顾了范式之后，我们发现赤字的上限是由到所谓的伪经典关联态的相对熵距离给出的，下限是纠缠的相对熵。这意味着，特别是，任何纠缠态是信息非局域的，即具有非零赤字。我们还应用该范式定义了消除纠缠的代价。我们表明，成本是有界的相对熵的纠缠从下面。我们证明了其他几个非局部现象的存在。例如，我们证明了存在一种形式的非局域性，没有纠缠和可并行性。我们分析了几类多体纯态的赤字，并得到与GHZ态相反，Aharonov态是非常非局域的（实际上可以被认为是准非局域化的）。我们还表明，不存在状态，赤字是严格等于整个信息内容（绑定本地信息）。然后，我们讨论分布式量子系统中的信息的互补特征。最后，我们讨论了结果的物理和理论意义，并提出了许多悬而未决的问题。

英文摘要：

In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm, we show that the upper bound for the deficit is given by the relative entropy distance to so-called psuedo-classically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal i.e. has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other non-local phenomena. For example,we prove the existence of a form of non-locality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal (and in fact can be thought of as quasi-nonlocalisable). We also show that there do not exist states, for which the deficit is strictly equal to the whole informational content (bound local information). We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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