Unbiased extremal rank-one measurements generate characterized randomness in dimension 2, with tetrahedral SIC having the least, and SICs achieve maximal 2 log d randomness device-dependently in dimensions where they exist.
Informationally complete measurements and groups representation
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abstract
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM's) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.
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quant-ph 1years
2026 1verdicts
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Quantum randomness beyond projective measurements
Unbiased extremal rank-one measurements generate characterized randomness in dimension 2, with tetrahedral SIC having the least, and SICs achieve maximal 2 log d randomness device-dependently in dimensions where they exist.