Distributed Quantum Faithful Simulation and Function Computation Using Algebraic Structured Measurements

We consider the task of faithfully simulating a distributed quantum measurement and function computation, and demonstrate a new achievable rate-region. For this, we develop the technique of randomly generating algebraic structured POVMs. To overcome the challenges caused by algebraic construction, we develop (i) a Pruning Trace inequality which is a tighter version of the known operator Markov inequality and (ii) a covering lemma which does not require the operator Chernoff inequality and hence applicable to pairwise-independent codewords. We demonstrate rate gains for this problem over traditional coding schemes and provide a multi-party distributed faithful simulation and function computation protocol.