Constructing all entanglement witnesses from density matrices

Journal Article · Fri Jul 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.014303· OSTI ID:22058800

Banghai, Wang ^[1]; Dongyang, Long ^[1]

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1. Department of Computer Science, Sun Yat-sen University, Guangzhou 510006 (China)

We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form W={rho}-c{sub {rho}}I, where {rho} is a density matrix, c{sub {rho}} is a non-negative number related to {rho}, and I is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamiolkowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provide the necessary and sufficient condition of the entanglement witness W={rho}-c{sub {rho}}I in operation, as well as in theory.

• OSTI ID: 22058800
• Journal Information: Physical Review. A, Vol. 84, Issue 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DENSITY MATRIX
QUANTUM ENTANGLEMENT
QUANTUM STATES