Renyi-Wehrl entropies as measures of localization in phase space

Details Renyi-Wehrl entropies as measures of localization in phase space Renyi-Wehrl entropies as measures of localization in phase space

2001-06-04

arxiv.org/abs/quant-ph/0106016v2

J. Phys. A: Math. Gen. 34, p. 10123-10139 (2001)

Physics

Quantum Physics

18 pages, no figures, some improved versions of main proofs, added J.reference

Scientific paper

10.1088/0305-4470/34/47/317

We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure states for spin systems. According to Lieb's conjecture the minimal values are provided by the spin coherent states. Though Lieb's conjecture remains unproven, we give new proofs of partial results that may be generalized for other systems. We also investigate random pure states and calculate the mean Renyi-Wehrl entropies averaged over the natural measure in the space of pure quantum states.

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