Limits on the Ability of Einstein-Podolsky-Rosen Pairs to Unambiguously Convey Classical Messages

In this paper, we consider two related problems, unambiguous discrimination of quantum mixed states and unambiguously conveying classical messages using Einstein-Podolsky-Rosen (EPR) pairs. The main technical contributions are as follows. First, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary N mixed quantum states with given a priori probability, which can be directly used to the unambiguous communication setting. Second, we propose a sufficient condition to show that a new upper bound can be achievable, and construct examples to clarify the relationship between the upper bound we derive and the existing upper bounds presented by other authors. Third, in the issue of conveying classical messages using EPR pairs, we also derive an upper bound on the success probability for unambiguously decoding, where Alice wants to convey n bit classical information to Bob by sending m quantum bits.