Lieb conjecture
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In quantum information theory, the Lieb conjecture is a theorem concerning the Wehrl entropy of quantum systems for which the classical phase space is a sphere. It states that no state of such a system has a lower Wehrl entropy than the SU(2) coherent states.
The analogous property for quantum systems for which the classical phase space is a plane was conjectured by Alfred Wehrl in 1978 and proven soon afterwards by Elliott H. Lieb,[1] who at the same time extended it to the SU(2) case. The conjecture was proven in 2012, by Lieb and Jan Philip Solovej.[2] The uniqueness of the minimizers was only proved in 2022 by Rupert L. Frank[3] and Aleksei Kulikov, Fabio Nicola, Joaquim Ortega-Cerda' and Paolo Tilli.[4]
References
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