• Corpus ID: 234763083

Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme

  title={Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme},
  author={Ludovico Lami and Maksim E. Shirokov},
The relative entropy of entanglement ER is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any state admits a (unique) closest separable state, even in infinite dimension; also, ER is everywhere lower semi-continuous. These results, which seem to have gone unnoticed so far, hold not only for the relative entropy of entanglement and its multi-partite… 
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