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

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

2007-06-20

arxiv.org/abs/0706.2907v1

Physics

Quantum Physics

This is a detailed proof of a result announced in quant-ph/0612050

Scientific paper

Consider many instances of an arbitrary quadripartite pure state of four quantum systems ACBR. Alice holds the AC part of each state, Bob holds B, while R represents all other parties correlated with ACB. Alice is required to redistribute the C systems to Bob while asymptotically retaining the purity of the global states. We prove that this is possible using Q qubits of communication and E ebits of shared entanglement between Alice and Bob provided that Q < I(R;C|B)/2 and Q + E < H(C|B). This matches the outer bound for this problem given in quant-ph/0611008. 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 subaddivity and uncover a general organizing principle, in analogy to thermodynamics, which underlies the optimal rates.

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