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arXiv · 2611.05317

Simple proof of conditions requiring maximal entanglement for local state verification and discrimination

Somshubhro Bandyopadhyay
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Abstract

For deterministic state verification by separable measurements, the Schmidt rank of an entangled resource must be at least that of the state being verified [N. Yu, R. Duan, and M. Ying, IEEE Trans. Inf. Theory 60, 2069 (2014)], and if the two are equal, the resource must be maximally entangled [S. Akibue, J. Miyazaki, and H. Osaka, Lett. Math. Phys. 116, 110 (2026)]. The latter was derived from a general theorem proved using algebraic geometry. In this paper, we give a simple, self-contained proof of both statements using only linear algebra. We then use these results to show that among pure entangled resources of local dimension at most $d$, a maximally entangled state of $\mathbb{C}^d\otimes\mathbb{C}^d$ is necessary and sufficient for perfect local discrimination of a generic orthogonal basis of $\mathbb{C}^d\otimes\mathbb{C}^d$, however weakly entangled. The same holds for local implementation of a generic orthogonal measurement.

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Somshubhro Bandyopadhyay. 2026-11-03. Simple proof of conditions requiring maximal entanglement for local state verification and discrimination. https://arxiv.org/abs/2611.05317

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