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

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