We introduce an algebraic measure of correlations in bipartite quantum systems. The proposed quantity, called maximal mutual correlation, provides the information how much a given state differs from the product state of its marginals. In contrast to the entanglement or quantum discord, maximal mutual correlation can be non - zero for some classically correlated quantum states.

arXiv:1607.06585Jul 22, 20160 citations

The European Physical Journal D

Maximal entanglement of bipartite spin states in the context of quantum algebra

K. Berrada, Y. Hassouni

Published Dec 3, 2010• 24 citations

Publisher

DOI: 10.1140/epjd/e2010-10479-1

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Lech Jakóbczyk

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A

for which

\det A = 0

implies unentanglement while

\det A \ne 0

implies entanglement. There is an underlying SU(2) algebra. (2) Teleportation for a general qubit state is possible by using non-maximally entangled bipartite qubit states. This protocol has an additional parameter, viz.,

\det A

, which enhances the cryptographic security of the teleportation. (c) For qutrits there is a matrix

P

for which

\det P = 0

simultaneously with

{\rm tr}P=\pm 1

imply unentanglement. Any departure from these conditions implies entanglement. There exists an underlying SU(3) algebra. (d) Physical interpretation of the underlying algebras are given and plausible experimental scenarios are proposed for the SU(2) case in the context of two entangled electrons. (e) The entanglement entropy in both cases, viz., for qubits and qutrits respectively, are expressed in terms of the determinants and trace of the matrices mentioned above.