Nonlocality, Asymmetry, and Distinguishing Bipartite States

Entanglement is a useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and what is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of $2\times 2$ quantum states to be locally distinguishable, and for a general set of $2\times n$ quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of “nonlocality without entanglement,” and we present a very simple proof of this phenomenon.