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

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.

arXiv:2611.05317 [quant-ph]

(or arXiv:2611.05317v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.05317 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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