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arXiv 1107.0355quant-phmath.FA
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利用局域非对易性检测量子关联

Detecting quantum correlations by means of local noncommutativity

Yu Guo, Jinchuan Hou

摘要:

量子关联是我们理解量子物理的关键。特别是在量子信息和量子计算中的强大应用。存在超越纠缠的量子关联,诸如量子不和谐(QD)和测量诱导的非定域性(MiN)[Phys.Rev.Lett. \textbf{106},120401(2011)]。在[Phys.Rev.A \textbf{77},022113(2008)]中,引入了PPT状态的一个子类,即所谓的强正部分转座(SPPT)状态,并且在那里证明了SPPT状态是可分离的。然而,在[Phys. Rev. A \textbf{81},064101(2010)]中用例子说明了该猜想是不正确的。本文将原SPPT看作到B部分的SPPT,定义了到A部分和B部分的SPPT态,并根据局部交换性给出了一类可分离的SPPT态,即超SPPT(SSPPT)态.此外,经典量子(CQ)状态和零的MiN的特点是通过局部交换性。基于CQ态,提出了无限维量子不和谐的几何测度(GMQD)。因此,我们强调MiN,QD(GMQD),SSPPT和分离性之间的关系,通过一个统一的方法为有限维和无限维系统:零MiN意味着零QD(GMQD),零QD(GMQD)信号SSPPT和SSPPT保证分离性,但反过来是无效的。

英文摘要:

Quantum correlation is a key to our understanding of quantum physics. In particular, it is essential for the powerful applications to quantum information and quantum computation. There exist quantum correlations beyond entanglement, such as quantum discord (QD) and measurement-induced nonlocality (MiN) [Phys. Rev. Lett. \textbf{106}, 120401(2011)]. In [Phys. Rev. A \textbf{77}, 022113(2008)], a subclass of PPT states so-called strong positive partial transposition (SPPT) states was introduced and it was conjectured there that SPPT states are separable. However, it was illustrated with examples in [Phys. Rev. A \textbf{81}, 064101(2010)] that this conjecture is not true. Viewing the original SPPT as SPPT up to part B, in the present paper, we define SPPT state up to part A and B respectively and present a separable class of SPPT states, that is the super SPPT (SSPPT) states, in terms of local commutativity. In addition, classical-quantum (CQ) states and nullity of MiN are characterized via local commutativity. Based on CQ states, the geometric measure of quantum discord (GMQD) for infinite-dimensional case is proposed. Consequently, we highlight the relation among MiN, QD(GMQD), SSPPT and separability through a unified approach for both finite- and infinite-dimensional systems: zero MiN implies zero QD(GMQD), zero QD(GMQD) signals SSPPT and SSPPT guarantees separability, but the converses are not valid.

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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