Optimal simulation of separable quantum measurements on bipartite states via likelihood POVMs

We focus on the information theoretic study of quantifying the information content in the outcome of a quantum measurement, also referred to as the measurement compression problem (MCP). The goal of this work is to develop a unified framework of tools to address this problem in diverse network scenarios both in the one-shot and asymptotic regimes. Designing a new measurement simulation protocol based on likelihood POVMs and developing analysis techniques based on a proxy state, we present a unified framework to derive the current known largest inner bounds for several network scenarios. Our findings include new one-shot inner bounds for the distributed MCP with and without quantum side information and the distributed quantum classical rate distortion problems.