Maximal entanglement versus entropy for mixed quantum states

By Tzu-Chieh Wei, Kae Nemoto, P. Goldbart, Paul G. Kwiat, William J. Munro, Frank Verstraete University of Illinois at Urbana-Champaign, U.S.A., Bangor University, U.K., Hewlett-Packard Laboratories and 3 more. 2002

271 citations recorded by the source corpus.

Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bc30abb481401333359c2be0d0858de56471c14d

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

The classical-quantum boundary for correlations: Discord and related measures (2011, background): “The maximally-discordant mixed states (MDMS) are defined in analogy to maximally-entangled mixed states (Munro et al., 2001; Wei et al., 2003).”
The role of quantum information in thermodynamics—a topical review (2015, background): “As a precursor to studying the possibility of entangling multipartite states, the complete solution for two qubits was found in [130] and later decent bounds on bipartite systems of arbitrary dimension were presented in [131].”
Searching for highly entangled multi-qubit states (2005, background): “We note that Wei et al (2003) have performed a more refined investigation of 2-qubit states, searching for the most entangled state (under various measures of entanglement) with given purity.”