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

## TL;DR

This paper develops a protocol for simulating distributed quantum measurements efficiently, characterizes the necessary communication resources, and applies these results to a distributed quantum rate-distortion problem.

## Contribution

It introduces a mutual covering lemma and a random binning technique for quantum measurements, enabling resource-efficient simulation and rate-distortion analysis.

## Key findings

- Characterized sufficient communication and randomness rates for asymptotic simulation.
- Developed a single-letter inner bound for the rate-distortion region.
- Provided an outer bound for the rate-distortion region using single-letterization.

## Abstract

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