Null dimension witness based on single measurements
arXiv:2305.08395 · doi:10.1103/PhysRevA.108.062202
Abstract
We present a null witness of the dimension of a quantum system, discriminating real, complex and classical spaces, based on equality due to linear independence. The witness involves only a single measurement with sufficiently many outcomes and prepared input states. In addition, for intermediate dimensions, the witness bounds saturate for a family of equiangular tight frames including symmetric informationally complete positive operator valued measures. Such a witness requires a minimum of resources, being robust against many practical imperfections. We also discuss errors due to finite statistics.
arXiv comment6 pages, 1 figure, 1 table
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