Optimal Visible Compression Rate For Mixed States Is Determined By Entanglement Of Purification

Abstract

Entanglement of purification was introduced by Terhal et al. for characterizing the bound of the generation of correlated states from maximally entangled states with sublinear size of classical communication. On the other hand, M. Horodecki obtained the optimal compression rate with a mixed states ensemble in the visible setting. In this paper, we prove that the optimal visible compression rate for mixed states is equal to the limit of the regularized entanglement of purification of the state corresponding to the given ensemble. This result gives a new interpretation to the entanglement of purification.

5 pages

References in corpus (3)

• The entanglement of purification
• A family of quantum protocols
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation

Cited by in corpus (7)

• Quantum Reverse Shannon Theorem
• Quantum rate distortion, reverse Shannon theorems, and source-channel separation
• Monogamy, polygamy, and other properties of entanglement of purification
• Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
• From Quantum Source Compression to Quantum Thermodynamics
• Rate Reduction of Blind Quantum Data Compression with Local Approximations Based on Unstable Structure of Quantum States
• Strongly non-quantitative classical information in quantum carriers