Distributed Quantum Faithful Simulation and Function Computation Using Algebraic Structured Measurements

In this work, we consider the task of faithfully simulating a distributed quantum measurement and function computation, and demonstrate a new achievable information-theoretic rate-region. For this, we develop the technique of randomly generating structured POVMs using algebraic codes. To overcome the challenges caused by algebraic construction, we develop a Pruning Trace inequality which is a tighter version of the known operator Markov inequality. In addition, we develop a covering lemma which is independent of the operator Chernoff inequality so as to be applicable for pairwise-independent codewords. We demonstrate rate gains for this problem over traditional coding schemes. Combining these techniques, we provide a multi-party distributed faithful simulation and function computation protocol.