Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance

Abstract

We resume the investigation of the problem of independent local compression of correlated quantum sources, the classical case of which is covered by the celebrated Slepian-Wolf theorem. We focus specifically on classical-quantum (cq) sources, for which one edge of the rate region, corresponding to the compression of the classical part, using the quantum part as side information at the decoder, was previously determined by Devetak and Winter [Phys. Rev. A 68, 042301 (2003)]. Whereas the Devetak-Winter protocol attains a rate-sum equal to the von Neumann entropy of the joint source, here we show that the full rate region is much more complex, due to the partially quantum nature of the source. In particular, in the opposite case of compressing the quantum part of the source, using the classical part as side information at the decoder, typically the rate sum is strictly larger than the von Neumann entropy of the total source. We determine the full rate region in the generic case, showing that, apart from the Devetak-Winter point, all other points in the achievable region have a rate sum strictly larger than the joint entropy. We can interpret the difference as the price paid for the quantum encoder being ignorant of the classical side information. In the general case, we give an achievable rate region, via protocols that are built on the decoupling principle, and the principles of quantum state merging and quantum state redistribution. Our achievable region is matched almost by a single-letter converse, which however still involves asymptotic errors and an unbounded auxiliary system.

arXiv comment21 pages, 4 figures

References in corpus (16)

• The information bottleneck method
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Quantum state merging and negative information
• The mother of all protocols: Restructuring quantum information's family tree
• Continuity of quantum conditional information
• A Resource Framework for Quantum Shannon Theory
• The exact cost of redistributing multipartite quantum states
• Classical data compression with quantum side information
• Optimal quantum source coding with quantum information at the encoder and decoder
• Coding Theorems of Quantum Information Theory
• A General Fidelity Limit for Quantum Channels
• State redistribution as merging: introducing the coherent relay
• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• On the distributed compression of quantum information
• Quantum Rate-Distortion Coding of Relevant Information

Cited by in corpus (8)

• Quantum communication on the bosonic loss-dephasing channel
• Strong converse bounds in quantum network information theory: distributed hypothesis testing and source coding
• One-Shot Hybrid State Redistribution
• From Quantum Source Compression to Quantum Thermodynamics
• Noisy quantum state redistribution with promise and the Alpha-bit
• A Rate-Distortion Perspective on Quantum State Redistribution
• Entanglement-Assisted Capacity of Quantum Channels with Side Information
• Classical State Masking over a Quantum Channel