Channel simulation with quantum side information

Abstract

We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classical-quantum Slepian-Wolf problem. The optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the Holevo information between the channel output and the quantum side information. Our main theorem has two important corollaries. The first is a quantum generalization of the Wyner-Ziv problem: rate-distortion theory with quantum side information. The second is an alternative proof of the trade-off between classical communication and common randomness distilled from a quantum state. The fully quantum generalization of the problem considered is quantum state redistribution. Here the sender and receiver share a mixed quantum state and the sender wants to transfer part of her state to the receiver using entanglement and quantum communication. We present outer and inner bounds on the achievable rate pairs.

22 pages, 3 figures

References in corpus (10)

• Quantum information can be negative
• Coding Theorem and Strong Converse for Quantum Channels
• Information transmission through a noisy quantum channel
• The mother of all protocols: Restructuring quantum information's family tree
• A family of quantum protocols
• Distilling common randomness from bipartite quantum states
• Classical data compression with quantum side information
• Compression of sources of probability distributions and density operators
• A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
• The capacity of a quantum channel for simultaneous transmission of classical and quantum information

Cited by in corpus (2)

• The exact cost of redistributing multipartite quantum states
• Secret Keys Assisted Private Classical Communication Capacity over Quantum Channels