More assistance of entanglement, less rounds of classical communication

Abstract

Abstract Classical communication plays a crucial role to distinguish locally a class of quantum states. Despite considerable advances, we have very little knowledge about the number of measurement and communication rounds needed to implement a discrimination task by local quantum operations and classical communications (in short, LOCC). In this paper, we are able to show the relation between round numbers with the local discrimination of a set of pure bipartite orthogonal quantum states. To demonstrate the possible strong dependence on the round numbers, we consider a class of orthogonal product states in d ⊗ d , which require at least 2 d − 2 round of classical communications. Curiously the round number can be reduced to d by the assistance of one-ebit of entanglement as resource and can be reduced further by assistance of more entanglement. We are also able to show that the number of LOCC rounds needed for a discrimination task may depend on the amount of entanglement assistance.