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arXiv · 2503.02568

Quantum state exclusion for group-generated ensembles of pure states

Arnau Diebra·Santiago Llorens·Emili Bagan·Gael Sentís·Ramon Muñoz-Tapia
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Abstract

Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups, establishing necessary and sufficient conditions for perfect (zero-error conclusive) exclusion. When perfect exclusion is impossible, we introduce two natural extensions: minimum-error and unambiguous exclusion. For both, we derive the optimal protocols and present analytical expressions for the corresponding failure probabilities and measurements, providing additional insight into how quantum states encode information.

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Arnau Diebra, Santiago Llorens, Emili Bagan, Gael Sentís, Ramon Muñoz-Tapia. 2025-03-04. Quantum state exclusion for group-generated ensembles of pure states. https://doi.org/10.1103/2k5d-bprn

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