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We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb in Invent Math 102(1):179-208, 1990).
Nonlinear programming
H. W. Kuhn and A. W. Tucker · 1951
Earlier work this paper cites.
A characterization of poisson processes
Alfréd Rényi · 1956
Earlier work this paper cites.
Norm Ideals of Completely Continuous Operators
R. Schatten · 1960
Earlier work this paper cites.
Thermodynamical proof of the gibbs formula for elementary quantum systems
A Lenard · 1978
Earlier work this paper cites.
Proof of an entropy conjecture of wehrl
Elliott H Lieb · 1978
Earlier work this paper cites.
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W Pusz and SL Woronowicz · 1978
Earlier work this paper cites.
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Alfred Wehrl · 1979
Earlier work this paper cites.
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J Gorecki and W Pusz · 1980
Earlier work this paper cites.
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Philip Hartman · 1982
Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
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