Faithful Simulation of Distributed Quantum Measurements with Applications in Distributed Rate-Distortion Theory
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We investigate faithful simulation of distributed quantum measurements as an extension of Winter's measurement compression theorem. We characterize a set of communication and common randomness rates needed to provide faithful simulation of distributed measurements. To achieve this, we introduce binning and mutual packing lemma for distributed quantum measurements. These techniques can be viewed as the quantum counterpart of their classical analogues. Finally, using these results, we develop a distributed quantum-to-classical rate distortion theory and characterize a rate region analogous to Berger-Tung's in terms of single-letter quantum mutual information quantities.
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