Efficient simulation of the dynamics of an n-dimensional PT-symmetric system with a local-operations-and-classical-communication protocol based on an embedding scheme

PT-symmetric quantum theory has attracted extensive attention in recent years because of its novel properties, applications, and even controversial discussions. Many difficulties in applications stem from the unknown of how to simulate the dynamics of PT-symmetric systems in conventional quantum systems. In this work, by clarifying some common confusion in the simulation of PT-symmetric systems, we are able to naturally extend the application scope of the original embedding simulation scheme from pure states to arbitrary mixed states. Based on the above groundwork, we further propose a local-operations-and-classical-communication (LOCC) protocol scheme to simulate the dynamics of a PT-symmetric system. Our LOCC protocol scheme, which needs one ancillary qubit only, can be applied to simulate any arbitrary finite-dimensional PT-symmetric system in the PT-unbroken phase and has several advantages over the original embedding scheme. The success probability is increased to lambda(min) (lambda(min) > 1) times in general, even approaching 100% in some special cases, and has a concise bound that makes it easier to estimate the necessary experimental resources in advance. Furthermore, our LOCC protocol has less dependence on but more flexibility in the selection of the metric operator and more adaptability in practical applications, and it is more consistent with the physical intuition. Finally, the physical or philosophical meaning behind the embedding scheme and the LOCC protocol is discussed.