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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20074 |
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| _version_ | 1866908793182355456 |
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| author | George, Ian Alhejji, Mohammad A. |
| author_facet | George, Ian Alhejji, Mohammad A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified George, Ian Alhejji, Mohammad A. Quantum Physics 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. |
| title | Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.20074 |