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We consider the task of faithfully simulating a distributed quantummeasurement, wherein we provide a protocol for the three parties, Alice, Boband Eve, to simulate a repeated action of a distributed quantum measurementusing a pair of non-product approximating measurements by Alice and Bob,followed by a stochastic mapping at Eve. The objective of the protocol is toutilize minimum resources, in terms of classical bits needed by Alice and Bobto communicate their measurement outcomes to Eve, and the common randomnessshared among the three parties, while faithfully simulating independentrepeated instances of the original measurement. To achieve this, we develop amutual covering lemma and a technique for random binning of distributed quantummeasurements, and, in turn, characterize a set of sufficient communication andcommon randomness rates required for asymptotic simulatability in terms ofsingle-letter quantum information quantities. Furthermore, using these resultswe address a distributed quantum rate-distortion problem, where we characterizethe achievable rate-distortion region through a single-letter inner bound.Finally, via a technique of single-letterization of multi-letter quantuminformation quantities, we provide an outer bound for the rate-distortionregion.

Faithful Simulation of Distributed Quantum Measurements with Applications in Distributed Rate-Distortion Theory