Genuine tripartite entanglement semi-monotone for (2 x 2 x n)-dimensional systems

Details Genuine tripartite entanglement semi-monotone for (2 x 2 x n)-dimensional systems Genuine tripartite entanglement semi-monotone for (2 x 2 x n)-dimensional systems

2006-07-05

arxiv.org/abs/quant-ph/0607032v2

Quantum Information and Computation 7(7),584 (2007)

Physics

Quantum Physics

11 pages, 1 figure. Replaced by revised version. To be published in Quantum Information and Computation

Scientific paper

In this paper, we present a new approach to study genuine tripartite entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximation technique. As applications, we give the analytic approximation for weakly mixed states, and study the genuine tripartite entanglement of two given weakly mixed states.

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