Entanglement measures and purification procedures

  title={Entanglement measures and purification procedures},
  author={Vlatko Vedral and M. B. Plenio},
  journal={Physical Review A},
We improve 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… 

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  • Rev. Lett. 78, 2275
  • 1997
submitted to Phys
  • Rev. A
  • 1997
  • Rev. A 54, 3824
  • 1996
  • Rev Lett. 78, 5022
  • 1997