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2017-04-01

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194749

On the Existence of Absolutely Maximally Entangled States of Minimal Support

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https://doi.org/10.18576/qpl/060101

Abstract

In this paper we prove that no absolutely maximally entangled, AME, state with minimal support exists with 7 sites and 5 levels. General AME states are pure multipartite states that, when reduced to half or less of the sites, the maximum entropy mixed state is obtained. They have found applications in teleportation and quantum secret sharing, and finding conditions for their existence is a well known open problem. We consider the version of this problem for minimally supported AME states. We single out known both sufficient and necessary conditions in that case. From our negative result, we show that the necessary condition is not sufficient. The proof uses a recent result on the theory of general, nonlinear, classical codes.

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Teoria quàntica

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Quantum theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BERNAL SERRANO, Antonio. On the Existence of Absolutely Maximally Entangled States of Minimal Support. Quantum Physics Letters. 2017. Vol. 6, num. 1, pags. 1-3. ISSN 2090-8318. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/194749

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