On bipartite pure-state entanglement structure in terms of disentanglement

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2375035· OSTI ID:20861549

Herbut, Fedor ^[1]

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1. Serbian Academy of Sciences and Arts, Knez Mihajlova 35, 11000 Belgrade (Serbia)

Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Philos. Soc. 31, 555 (1935)], i.e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in investigating the qualitative side of entanglement in any bipartite state vector. Remote measurement (or, equivalently, remote orthogonal state decomposition) from previous work is generalized to remote linearly independent complete state decomposition both in the nonselective and the selective versions. The results are displayed in terms of commutative square diagrams, which show the power and beauty of the physical meaning of the (antiunitary) correlation operator inherent in the given bipartite state vector. This operator, together with the subsystem states (reduced density operators), constitutes the so-called correlated subsystem picture. It is the central part of the antilinear representation of a bipartite state vector, and it is a kind of core of its entanglement structure. The generalization of previously elaborated disentanglement expounded in this article is a synthesis of the antilinear representation of bipartite state vectors, which is reviewed, and the relevant results of [Cassinelli et al., J. Math. Anal. Appl. 210, 472 (1997)] in mathematical analysis, which are summed up. Linearly independent bases (finite or infinite) are shown to be almost as useful in some quantum mechanical studies as orthonormal ones. Finally, it is shown that linearly independent remote pure-state preparation carries the highest probability of occurrence. This singles out linearly independent remote influence from all possible ones.

• OSTI ID: 20861549
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATIONS
PROBABILITY
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SCHROEDINGER EQUATION
VECTORS