TY - JOUR

T1 - Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

AU - H. Lieb, Elliott

AU - Solovej, Jan Philip

PY - 2014

Y1 - 2014

N2 - Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum $J$. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1, ...$, with $K=\infty$ corresponding to the Wehrl map to classical densities. For each $J$ and $J

AB - Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum $J$. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1, ...$, with $K=\infty$ corresponding to the Wehrl map to classical densities. For each $J$ and $J

KW - math-ph

KW - cond-mat.stat-mech

KW - math.MP

KW - quant-ph

U2 - 10.1007/s11511-014-0113-6

DO - 10.1007/s11511-014-0113-6

M3 - Journal article

VL - 212

SP - 379

JO - Acta Mathematica

JF - Acta Mathematica

SN - 0001-5962

IS - 2

ER -