Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified

Abstract

In a seminal work [PRL85.4972], Walgate, Short, Hardy, and Vedral prove in finite dimensions that for every pair of pure multipartite orthogonal quantum states, there exists a one-way local operations and classical communication (LOCC) protocol that perfectly distinguishes the pair. We extend this result to infinite dimensions with a simpler proof. For states on ${\mathbb{C}}^{d_A\times d_A}\otimes {\mathbb{C}}^{d_B\times d_B}$, we strengthen this existence result by constructing an $O(d_A^2{d}_B^2)$-time algorithm that specifies such a perfect one-way LOCC protocol. Finally, we establish the equivalence between Walgate et al.'s result and the fact that the one-shot environment-assisted classical capacity of every quantum channel is at least 1 bit per channel use, thereby clarifying the literature on these notions. At the core of all of these results is the fact that every operator with vanishing trace admits a basis where its diagonal entries are all zero.

arXiv comment8 pages, 2 figures, comments welcome