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arXiv · 0706.2907

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

Jon Yard·Igor Devetak
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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.

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Jon Yard, Igor Devetak. 2007-06-20. Optimal quantum source coding with quantum information at the encoder and decoder. https://doi.org/10.1109/tit.2009.2030494

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