Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
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Proof of an entropy conjecture for Bloch coherent spin states and its generalizations. / H. Lieb, Elliott; Solovej, Jan Philip.
I: Acta Mathematica, Bind 212, Nr. 2, 2014, s. 379.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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 -
ID: 117077559