Classical Tensors and Quantum Entanglement II: Mixed States

Details Classical Tensors and Quantum Entanglement II: Mixed States Classical Tensors and Quantum Entanglement II: Mixed States

2010-11-26

arxiv.org/abs/1011.5859v2

Int.J.Geom.Meth.Mod.Phys.08:853-883,2011

Physics

Mathematical Physics

23 pages, 4 figures

Scientific paper

10.1142/S0219887811005439

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.

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