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Information-theoretic aspects of Werner states
Li, Nan1,2; Luo, Shunlong1,2; Sun, Yuan3
Source PublicationANNALS OF PHYSICS
AbstractIn 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. (C) 2020 Elsevier Inc. All rights reserved.
KeywordWerner states Quantum correlations Wigner-Yanase skew information Unitary group Quantum uncertainty Total uncertainty
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[11775298] ; National Natural Science Foundation of China[11875317] ; National Natural Science Foundation of China[12005104] ; National Natural Science Foundation of China[61833010] ; Youth Innovation Promotion Association of CAS, China[2020002]
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000608112400007
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Document Type期刊论文
Corresponding AuthorLuo, Shunlong
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China
Recommended Citation
GB/T 7714
Li, Nan,Luo, Shunlong,Sun, Yuan. Information-theoretic aspects of Werner states[J]. ANNALS OF PHYSICS,2021,424:16.
APA Li, Nan,Luo, Shunlong,&Sun, Yuan.(2021).Information-theoretic aspects of Werner states.ANNALS OF PHYSICS,424,16.
MLA Li, Nan,et al."Information-theoretic aspects of Werner states".ANNALS OF PHYSICS 424(2021):16.
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