Entanglement measures and approximate quantum error correction

Abstract

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.

7 pages, two-columned revtex4, no figures. v1: Deeply revised and extended version: different entanglement measures are separately considered, references are added, and some remarks are stressed. v2: Added a sufficient condition for distillability in terms of entanglement of formation; published version

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• Information preserving structures: A general framework for quantum zero-error information
• A simple approach to approximate quantum error correction based on the transpose channel
• Approximate simulation of quantum channels
• Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries
• Tight Bounds on the Accessible Information and the Informational Power
• Accessible Information and Informational Power of Quantum 2-designs
• Private quantum decoupling and secure disposal of information
• Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition
• Irreversibility of entanglement loss