A Lower Bound for the Wehrl Entropy of Quantum Spin with Sharp High-Spin Asymptotics

Bodmann, Bernhard G.

doi:10.1007/s00220-004-1146-z

Cited by 8 publications

(9 citation statements)

References 35 publications

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“…3.1]). An analogous result was proven for the Fock space in [14], and a similar result also appears in [7].…”

Section: Contractive Inclusions Of Bergman Spacessupporting

confidence: 73%

“…We now begin the proof of Theorem 1. A version of it was announced in [4] 1 , following a scheme designed in [7]. Observe also that an analogous result in the Fock space was proved by Carlen [14] using a logarithmic Sobolev inequality.…”

Section: Contractive Inclusions Of Bergman Spacesmentioning

confidence: 94%

“…for example by computing by coefficients. If f is a non-vanishing function of H 1 (D), writing f = gh with g = h = f 1/2 now leads to (7). For a general function f ∈ H 1 (D), we first factor out the zeroes through a Blaschke product.…”

Section: Contractive Inclusions Of Bergman Spacesmentioning

confidence: 99%

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Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Bayart

Brevig

Haimi

et al. 2018

Trans. Amer. Math. Soc.

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We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield corresponding inequalities for the Bergman spaces of Dirichlet series. We use these results to study weighted multiplicative Hankel forms associated with the Bergman spaces of Dirichlet series, reproducing most of the known results on multiplicative Hankel forms associated with the Hardy spaces of Dirichlet series. In addition, we find a direct relationship between the two type of forms which does not exist in lower dimensions. Finally, we produce some counter-examples concerning Carleson measures on the infinite polydisc.

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“…3.1]). An analogous result was proven for the Fock space in [14], and a similar result also appears in [7].…”

Section: Contractive Inclusions Of Bergman Spacessupporting

confidence: 73%

Section: Contractive Inclusions Of Bergman Spacesmentioning

confidence: 94%

See 1 more Smart Citation

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Bayart

Brevig

Haimi

et al. 2018

Trans. Amer. Math. Soc.

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“…He stated the conjecture only for Glauber coherent states on L 2 (R n ), and this was proved shortly thereafter in [13], in which the conjecture was extended to SU (2). This SU(2) conjecture was finally settled by us 35 years later [15], although there were several special cases proved earlier [3,8,16,17,18,19]. c 2015 by the authors.…”

Section: Introductionmentioning

confidence: 98%

Proof of the Wehrl-type Entropy Conjecture for Symmetric $${SU(N)}$$ Coherent States

Lieb

Solovej

2016

Commun. Math. Phys.

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The Wehrl entropy conjecture for coherent (highest weight) states in representations of the Heisenberg group, which was proved in 1978 and recently extended by us to the group SU (2), is further extended here to symmetric representations of the groups SU (N ) for all N . This result gives further evidence for our conjecture that highest weight states minimize group integrals of certain concave functions for a large class of Lie groups and their representations.

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“…For the 3-dimensional case of spin 1 the conjecture was solved by Scutaru [13] and by Schupp [12] who also solved it for the 4-dimensional representation corresponding to spin 3/2. Bodmann [3] proved a lower bound on the classical entropy which is asymptotically correct for large spin J.…”

Section: Introductionmentioning

confidence: 99%

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

Lieb

Solovej

2014

Acta Math.

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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 = ∞ corresponding to the Wehrl map to classical densities. For each J and J < K ≤ ∞ we show that the minimal output entropy for these channels occurs for a J coherent state. We also show that coherent states both Glauber and Bloch minimize any concave functional, not just entropy. c 2012 by the authors. This article may be reproduced in its entirety for non-commercial purposes.EHLJPS-September 22, 2012-coherent states and entropy for some complex scalar µ ′ . Here we have used that J ω ω K = |ω K−J in H K−J ⊗ H J , sinceMoreover, U J η has no component in the space ω · S J = J, hence J U J η ω K = 0 and thus P − |ω ′ with µ = (−1) 2J µ ′ , which is what we wanted to prove.

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A Lower Bound for the Wehrl Entropy of Quantum Spin with Sharp High-Spin Asymptotics

Cited by 8 publications

References 35 publications

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Proof of the Wehrl-type Entropy Conjecture for Symmetric $${SU(N)}$$ Coherent States

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

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