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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Renyi squashed entanglement, discord, and relative entropy differences
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Renyi squashed entanglement, discord, and relative entropy differences

机译：仁义压缩纠缠，不和谐和相对熵的差异

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摘要

The squashed entanglement quantifies the amount of entanglement in a bipartite quantum state, and it satisfies all of the axioms desired for an entanglement measure. The quantum discord is a measure of quantum correlations that are different from those due to entanglement. What these two measures have in common is that they are both based upon the conditional quantum mutual information. In Berta et al (2015 J. Math. Phys. 56 022205), we recently proposed Renyi generalizations of the conditional quantum mutual information of a tripartite state on ABC (with C being the conditioning system), which were shown to satisfy some properties that hold for the original quantity, such as non-negativity, duality, and monotonicity with respect to local operations on the system B (with it being left open to show that the Renyi quantity is monotone with respect to local operations on system A). Here we define a Renyi squashed entanglement and a Renyi quantum discord based on a Renyi conditional quantum mutual information and investigate these quantities in detail. Taking as a conjecture that the Renyi conditional quantum mutual information is monotone with respect to local operations on both systems A and B, we prove that the Renyi squashed entanglement and the Renyi quantum discord satisfy many of the properties of the respective original von Neumann entropy based quantities. In our prior work (Berta et al 2015 Phys. Rev. A 91 022333), we also detailed a procedure to obtain Renyi generalizations of any quantum information measure that is equal to a linear combination of von Neumann entropies with coefficients chosen from the set {-1, 0, 1}. Here, we extend this procedure to include differences of relative entropies. Using the extended procedure and a conjectured monotonicity of the Renyi generalizations in the Renyi parameter, we discuss potential remainder terms for well known inequalities such as monotonicity of the relative entropy, joint convexity of the relative entropy, and the Holevo bound.
机译：压扁的纠缠量化了二分量子态下的纠缠量，并且满足了纠缠测度所需的所有公理。量子失调是对量子相关性的一种度量，该量子相关性与纠缠导致的相关性不同。这两种措施的共同之处在于它们都基于条件量子互信息。在Berta等人（2015 J. Math。Phys。56 022205）中，我们最近提出了ABC上三方态的条件量子互信息的Renyi推广（以C为条件系统），证明其满足某些特性保持原始数量，例如相对于系统B上本地操作的非负性，对偶性和单调性（将其打开以表明Renyi量相对于系统A上本地操作是单调的）。在这里，我们根据人一条件量子互信息定义人一挤压纠缠和人一量子不和，并详细研究这些量。假设Renyi条件量子互信息相对于系统A和B上的局部运算是单调的，我们证明Renyi压缩纠缠和Renyi量子不和谐满足各自原始von Neumann熵的许多性质数量。在我们之前的工作中（Berta等人，2015年，Phys。Rev. A 91 022333），我们还详细介绍了一种程序，该程序可获取等于von Neumann熵与系数的线性组合的任何量子信息量度的Renyi概括{ -1，0，1}。在这里，我们将这一过程扩展到包括相对熵的差异。使用扩展过程和Renyi参数中Renyi泛化的猜想单调性，我们讨论了众所周知的不等式的潜在余项，例如相对熵的单调性，相对熵的联合凸性和Holevo界。

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