quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...

theory, the Lieb conjecture is a theorem concerning the

Wehrl entropy In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability di ...

of quantum systems for which the classical

phase space In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually ...

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

is a ''plane'' was conjectured by Alfred Wehrl in 1978 and proven soon afterwards by

Elliott H. Lieb Elliott Hershel Lieb (born July 31, 1932) is an American mathematical physics#Mathematically rigorous physics, mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, Cond ...

, 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 Jan Philip Solovej (born 14 June 1961) is a Danish mathematician and mathematical physicist working on the mathematical theory of quantum mechanics. He is a professor at University of Copenhagen. Biography Solovej obtained his Ph.D. in 198 ...

References

External links

Video of a lecture by Lieb discussing the conjecture and outlining its proof.
Quantum mechanical entropy Conjectures that have been proved {{quantum-stub