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Maximal entanglement versus entropy for mixed quantum states

Wei, Tzu-Chieh; Nemoto, Kae; Goldbart, Paul M.; Kwiat, Paul G.; Munro, William J.; Verstraete Frank

HPL-2002-344

Keyword(s): quantum information; coherent pulses; quantum gate

Abstract: 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. Notes: Tzu-Chieh Wei, Paul M. Goldbart & Paul G. Kwiat, Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA Kae Nemoto, School of Informatics, Bangor University, Bangor LL57 1UT, UK Frank Verstraete, Department of Mathematical Physics and Astronomy, Ghent University, Belgium

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