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Information-theoretic aspects of Werner states
Annals of Physics ( IF 3.0 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.aop.2020.168371
Nan Li , Shunlong Luo , Yuan Sun

Abstract In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner-Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

中文翻译:

维尔纳状态的信息论方面

摘要 在爱因斯坦-波多尔斯基-罗森相关(纠缠)的量子态的开创性研究中,承认一个隐藏变量模型(Werner,1989),Werner 引入了纠缠/可分离性的二分法,并设计了一个高度对称的状态族,现在称为维尔纳状态,其中一些表现出纠缠但没有贝尔非局域性。事实证明,维尔纳态具有丰富的相关结构,构成了一种范式,在量子信息的理论和实验探索中都发挥了创新作用。鉴于维尔纳态的理论意义和广泛应用,我们首先简要回顾维尔纳态的信息内容,然后根据 Wigner-Yanase 偏斜信息对其进行信息论表征:Werner 态被确定为相对于自然可观测族(即对角幺正群的生成元)具有最小量子不确定性的状态。为此,我们引入了一种对研究不对称性、相干性和不确定性具有独立兴趣的量子不确定性度量,并揭示了其基本特性。我们进一步将贝尔三重态确定为维尔纳态的相反态,因为它们具有最大量的量子不确定性。类似地,我们将各向同性状态作为最小量子不确定状态的类似特征提供给密切相关的算子族。对角酉群的生成元)。为此,我们引入了一种对研究不对称性、相干性和不确定性具有独立兴趣的量子不确定性度量,并揭示了其基本特性。我们进一步将贝尔三重态确定为维尔纳态的相反态,因为它们具有最大量的量子不确定性。类似地,我们将各向同性状态作为最小量子不确定状态的类似特征提供给密切相关的算子族。对角酉群的生成元)。为此,我们引入了一种对研究不对称性、相干性和不确定性具有独立兴趣的量子不确定性度量,并揭示了其基本特性。我们进一步将贝尔三重态确定为维尔纳态的相反态,因为它们具有最大量的量子不确定性。类似地,我们将各向同性状态作为最小量子不确定性状态提供了与密切相关的算子族类似的表征。我们进一步将贝尔三重态确定为维尔纳态的相反态,因为它们具有最大量的量子不确定性。类似地,我们将各向同性状态作为最小量子不确定性状态提供了与密切相关的算子族类似的表征。我们进一步将贝尔三重态确定为维尔纳态的相反态,因为它们具有最大量的量子不确定性。类似地,我们将各向同性状态作为最小量子不确定状态的类似特征提供给密切相关的算子族。
更新日期:2021-01-01
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