Entanglement measures and approximate quantum error correction

Details Entanglement measures and approximate quantum error correction Entanglement measures and approximate quantum error correction

2007-06-13

arxiv.org/abs/0706.1815v3

Phys. Rev. A 77, 012309 (2008)

Physics

Quantum Physics

7 pages, two-columned revtex4, no figures. v1: Deeply revised and extended version: different entanglement measures are separa

Scientific paper

10.1103/PhysRevA.77.012309

It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a byproduct, we prove a bound quantifying how large the gap between entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in terms of entanglement of formation.

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