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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.7 No.7
September 2007 |
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Separability criteria based on the Bloch representation of
density matrices
(pp624-638)
Julio
de Vicente
doi:
https://doi.org/10.26421/QIC7.7-5
Abstracts:
We study the separability of bipartite quantum systems in
arbitrary dimensions using the Bloch representation of their density
matrix. This approach enables us to find an alternative characterization
of the separability problem, from which we derive a necessary condition
and sufficient conditions for separability. For a certain class of
states the necessary condition and a sufficient condition turn out to be
equivalent, therefore yielding a necessary and sufficient condition. The
proofs of the sufficient conditions are constructive, thus providing
decompositions in pure product states for the states that satisfy them.
We provide examples that show the ability of these conditions to detect
entanglement. In particular, the necessary condition is proved to be
strong enough to detect bound entangled states.
Key words:
Bloch representation, entanglement,
bipartite quantum systems |
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