Entanglement Measures and Purification Procedures

Details Entanglement Measures and Purification Procedures Entanglement Measures and Purification Procedures

1997-07-17

arxiv.org/abs/quant-ph/9707035v2

Phys. Rev. A57:1619-1633,1998

Physics

Quantum Physics

40 pages, 2 figures, small changes, included references to Lieb and Ruskai for the proof of strong subadditivity

Scientific paper

10.1103/PhysRevA.57.1619

We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure which have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the Quantum Relative Entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure and that distillable entanglement is in general smaller than the entanglement of creation.

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