Local purity distillation with bounded classical communication

Abstract

Local pure states are an important resource for quantum computing. The problem of distilling local pure states from mixed ones can be cast in an information theoretic paradigm. The bipartite version of this problem where local purity must be distilled from an arbitrary quantum state shared between two parties, Alice and Bob, is closely related to the problem of separating quantum and classical correlations in the state and in particular, to a measure of classical correlations called the one-way distillable common randomness. In Phys. Rev. A 71, 062303 (2005), the optimal rate of local purity distillation is derived when many copies of a bipartite quantum state are shared between Alice and Bob, and the parties are allowed unlimited use of a unidirectional dephasing channel. In the present paper, we extend this result to the setting in which the use of the channel is bounded. We demonstrate that in the case of a classical-quantum system, the expression for the local purity distilled is efficiently computable and provide examples with their tradeoff curves.

9 pages and 2 figure in .eps

References in corpus (12)

• Classical, quantum and total correlations
• Distillation of secret key and entanglement from quantum states
• A Thermodynamical Approach to Quantifying Quantum Correlations
• Reversible transformations from pure to mixed states, and the unique measure of information
• A Resource Framework for Quantum Shannon Theory
• Information as a resource in distributed quantum systems
• Remote preparation of quantum states
• Distilling common randomness from bipartite quantum states
• "Extrinsic" and "intrinsic" data in quantum measurements: asymptotic convex decomposition of positive operator valued measures
• Distillation of local purity from quantum states
• A new type of complementarity between quantum and classical information
• Trading quantum for classical resources in quantum data compression

Cited by in corpus (6)

• Entanglement-assisted communication of classical and quantum information
• The information-theoretic costs of simulating quantum measurements
• Entropy of a quantum channel
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• Fidelity-Based Smooth Min-Relative Entropy: Properties and Applications
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States