Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified

• URL: http://arxiv.org/abs/2601.20074v1
• Date: Tue, 27 Jan 2026 21:36:27 GMT
• Title: Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified
• Authors: Ian George, Mohammad A. Alhejji,
• Abstract summary: Walgate, Short, Hardy, and Vedral prove in finite dimensions that there exists a one-way local operations and classical communication protocol.<n>We extend this result to infinite dimensions with a simpler proof.<n>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.
• Score: 1.2891210250935148
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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