Verifying randomness in sets of quantum states via observables

• URL: http://arxiv.org/abs/2404.16211v1
• Date: Wed, 24 Apr 2024 21:11:58 GMT
• Title: Verifying randomness in sets of quantum states via observables
• Authors: Xavier Bonet-Monroig, Hao Wang, Adrián Pérez-Salinas,
• Abstract summary: We show that Haar-randomness is connected to the Dirichlet distribution, and provide a closed-form expression, and simple bounds of the statistical moments. We generalize this metric to permutation- and unitary-equivalent observables, ensuring that if the extended average randomness is compatible with a Haar-random distribution, then the set of states is approximately Haar-random.
• Score: 4.289151408389622
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a metric, average randomness, that predicts the compatibility of a set of quantum states with the Haar-random distribution, by matching of statistical moments, through a known quantum observable. We show that Haar-randomness is connected to the Dirichlet distribution, and provide a closed-form expression, and simple bounds of the statistical moments. We generalize this metric to permutation- and unitary-equivalent observables, ensuring that if the extended average randomness is compatible with a Haar-random distribution, then the set of states is approximately Haar-random.

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