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arXiv · 1704.04609

Quantum measurements with prescribed symmetry

W. Bruzda·D. Goyeneche·K. Życzkowski
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Abstract

We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.

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W. Bruzda, D. Goyeneche, K. Życzkowski. 2017-07-05. Quantum measurements with prescribed symmetry. https://doi.org/10.1103/physreva.96.022105

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