Difficulties in analytic computation for relative entropy of entanglement

Journal Article · Sat May 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.052325· OSTI ID:21408799

Kim, Hungsoo ^[1]; Hwang, Mi-Ra; Jung, Eylee ^[2]; Park, DaeKil ^[2]

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1. Institute of Basic Science, Kyungnam University, Masan 631-701 (Korea, Republic of)
2. Department of Physics, Kyungnam University, Masan 631-701 (Korea, Republic of)

It is known that relative entropy of entanglement for an entangled state {rho} is defined via its closest separable (or positive partial transpose) state {sigma}. Recently, it has been shown how to find {rho} provided that {sigma} is given in a two-qubit system. In this article we study the reverse process, that is, how to find {sigma} provided that {rho} is given. It is shown that if {rho} is of a Bell-diagonal, generalized Vedral-Plenio, or generalized Horodecki state, one can find {sigma} from a geometrical point of view. This is possible due to the following two facts: (i) the Bloch vectors of {rho} and {sigma} are identical to each other; (ii) the correlation vector of {sigma} can be computed from a crossing point between a minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the correlation vector of {rho} and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these properties are not maintained for the arbitrary two-qubit states.

• OSTI ID: 21408799
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
CORRELATIONS
ENTROPY
PHYSICAL PROPERTIES
QUANTUM ENTANGLEMENT
TENSORS
THERMODYNAMIC PROPERTIES
VECTORS