On the distributed compression of quantum information

Abstract

We consider the problem of distributed compression for correlated quantum sources. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. We show that, in general, this is not the case for quantum sources by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Here we find optimal non-trivial strategies for a different extreme, sources of Bell states. In addition, we illustrate how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

15 pages. v3 corrects an error in the section on irreducible product sources

References in corpus (12)

• Mixed State Entanglement and Quantum Error Correction
• Good Quantum Error-Correcting Codes Exist
• Quantum state transfer and entanglement distribution among distant nodes in a quantum network
• Quantum information can be negative
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Codes for the Quantum Erasure Channel
• The mother of all protocols: Restructuring quantum information's family tree
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• Coding Theorems of Quantum Information Theory
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Cited by in corpus (14)

• Quantum information can be negative
• The mother of all protocols: Restructuring quantum information's family tree
• Optical Interferometry with Quantum Networks
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• Distributed Compression and Multiparty Squashed Entanglement
• Simultaneous classical-quantum capacities of quantum multiple access channels
• Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance
• Capacity Theorems for Quantum Multiple Access Channels
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• From Quantum Source Compression to Quantum Thermodynamics
• One-shot Multiparty State Merging
• Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation
• Distributed Compression and Squashed Entanglement
• A Rate-Distortion Perspective on Quantum State Redistribution