Lieb conjecture

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 only proven in 2012, by Lieb and Jan Philip Solovej.[2]

References

Lieb, Elliott H. (August 1978). "Proof of an entropy conjecture of Wehrl". Communications in Mathematical Physics. 62 (1): 35–41. Bibcode:1978CMaPh..62...35L. doi:10.1007/BF01940328. S2CID 189836756.
Lieb, Elliott H.; Solovej, Jan Philip (17 May 2014). "Proof of an entropy conjecture for Bloch coherent spin states and its generalizations". Acta Mathematica. 212 (2): 379–398. arXiv:1208.3632. doi:10.1007/s11511-014-0113-6. S2CID 119166106.

External links

Video of a lecture by Lieb discussing the conjecture and outlining its proof.

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[1] Lieb, Elliott H. (August 1978). "Proof of an entropy conjecture of Wehrl". Communications in Mathematical Physics. 62 (1): 35–41. Bibcode:1978CMaPh..62...35L. doi:10.1007/BF01940328. S2CID 189836756.

[2] Lieb, Elliott H.; Solovej, Jan Philip (17 May 2014). "Proof of an entropy conjecture for Bloch coherent spin states and its generalizations". Acta Mathematica. 212 (2): 379–398. arXiv:1208.3632. doi:10.1007/s11511-014-0113-6. S2CID 119166106.