Optimal Simulation of Quantum Measurements via the Likelihood POVMs

We provide a new and simplified proof of Winter's measurement compression [2004] via likelihood POVMs. Secondly, we provide an alternate proof of the central tool at the heart of this theorem - the Quantum covering lemma - that does not rely on the Ahlswede Winter's operator Chernoff bound [2002], thereby requires only pairwise independence of the involved random operators. We leverage these results to design structured POVMs and prove their optimality in regards to communication rates.