Optimal quantum source coding with quantum information at the encoder and decoder

TL;DR

This paper establishes the optimal quantum source coding rates for redistributing quantum systems between parties, providing an operational interpretation of quantum conditional mutual information and linking to fundamental quantum information principles.

Contribution

It proves the optimal rates for quantum source coding with shared entanglement, confirming the Luo-Devetak bound and offering a new operational meaning for quantum conditional mutual information.

Findings

Optimal qubit rate Q >= I(C;D|B)/2

Total rate Q + E >= H(C|B)

Operational proof of strong subadditivity

Abstract

Consider many instances of an arbitrary quadripartite pure state of four quantum systems ABCD. Alice holds the AC part of each state, Bob holds B, while D represents all other parties correlated with ABC. Alice is required to redistribute the C systems to Bob while asymptotically preserving the overall purity. We prove that this is possible using Q qubits of communication and E ebits of shared entanglement between Alice and Bob, provided that Q geq I(C;D|B)/2 and Q+E geq H(C|B), proving the optimality of the Luo-Devetak outer bound. The optimal qubit rate provides the first known operational interpretation of quantum conditional mutual information. We also show how our protocol leads to a fully operational proof of strong subadditivity and uncover a general organizing principle, in analogy to thermodynamics, that underlies the optimal rates.