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• W2949661176 abstract "We introduce a notion of matrix valued Gram decompositions for correlation matrices whose study is motivated by quantum information theory. We show that for extremal correlations, the matrices in such a factorization generate a Clifford algebra and thus, their size is exponential in terms of the rank of the correlation matrix. Using this we give a self-contained and succinct proof of the existence of completely positive semidefinite matrices with sub-exponential cpsd-rank, recently derived in the literature. This fact also underlies and generalizes Tsirelson's seminal lower bound on the local dimension of a quantum system necessary to generate an extreme quantum correlation." @default.
• W2949661176 created "2019-06-27" @default.
• W2949661176 creator A5078214509 @default.
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• W2949661176 date "2017-02-21" @default.
• W2949661176 modified "2023-09-27" @default.
• W2949661176 title "Correlation matrices, Clifford algebras, and completely positive semidefinite rank" @default.
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