Remarks on the Equivalence of Full Additivity and Monotonicity for the Entanglement Cost

  • Authors:

  • F. G. Brandão;M. Horodecki;M. B. Plenio;S. Virmani

  • Affiliations:

  • QOLS, Blackett Laboratory, Imperial College London, London, UK SW7 2BW and Institute for Mathematical Sciences, Imperial College London, London, UK SW7 2BW;Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Gdansk, Poland;QOLS, Blackett Laboratory, Imperial College London, London, UK SW7 2BW and Institute for Mathematical Sciences, Imperial College London, London, UK SW7 2BW;QOLS, Blackett Laboratory, Imperial College London, London, UK SW7 2BW and Institute for Mathematical Sciences, Imperial College London, London, UK SW7 2BW

  • Venue:
  • Open Systems & Information Dynamics
  • Year:
  • 2007

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Abstract

We analyse the relationship between the full additivity of the entanglement cost and its full monotonicity under local operations and classical communication. We show that the two properties are equivalent for the entanglement cost. The proof works for the regularization of any convex, subadditive, and asymptotically continuous entanglement monotone, and hence also applies to the asymptotic relative entropy of entanglement.