Mixed-state entanglement and quantum communication

Abstract

We present basics of mixed-state entanglement theory. The first part of the article is devoted to mathematical characterizations of entangled states. In second part we discuss the question of using mixed-state entanglement for quantum communication. In particular, a type of entanglement that is not directly useful for quantum communcation (called bound entanglement) is analysed in detail.

42 pages; the article is part of a book entitled {\it Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments} by G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rotteler, H. Weinfurter, R. Werner and A. Zeilinger, published in {\it Springer Tracts in Modern Physics}, July 2001

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• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• Entanglement and Relativity
• Quantum dynamical semigroups and non-decomposable positive maps
• Sufficient separability criteria and linear maps
• Geometric discord and Measurement-induced nonlocality for well known bound entangled states
• Slipped non-Positive Reduced Dynamics and Entanglement
• Immense Fidelity Enhancement of Encoded Quantum Bell Pairs at Short and Long-distance Communication along with Generalized Design of Circuit
• Quantum Teleportation: from Pure to Mixed States and Standard to Optimal