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Device-independent tests of classical and quantum dimensions

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arxiv 1010.5064 v1 pith:D4VBRCZU submitted 2010-10-25 quant-ph

Device-independent tests of classical and quantum dimensions

classification quant-ph
keywords quantumclassicaldimensiondatalowernecessaryproblemreproduce
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalise the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

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