The Wehrl entropy has Gaussian optimizers
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The Wehrl entropy has Gaussian optimizers. / de Palma, Giacomo.
I: Letters in Mathematical Physics, Bind 108, Nr. 1, 01.01.2018, s. 97-116.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The Wehrl entropy has Gaussian optimizers
AU - de Palma, Giacomo
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel that associates with a quantum state its Husimi Q representation is asymptotically equivalent to the Gaussian quantum-limited amplifier with infinite amplification parameter. This equivalence also permits to determine the p→ q norms of the aforementioned quantum-classical channel in the two particular cases of one mode and p= q and prove that they are achieved by thermal Gaussian states. The same equivalence permits to prove that the Husimi Q representation of a one-mode passive state (i.e., a state diagonal in the Fock basis with eigenvalues decreasing as the energy increases) majorizes the Husimi Q representation of any other one-mode state with the same spectrum, i.e., it maximizes any convex functional.
AB - We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel that associates with a quantum state its Husimi Q representation is asymptotically equivalent to the Gaussian quantum-limited amplifier with infinite amplification parameter. This equivalence also permits to determine the p→ q norms of the aforementioned quantum-classical channel in the two particular cases of one mode and p= q and prove that they are achieved by thermal Gaussian states. The same equivalence permits to prove that the Husimi Q representation of a one-mode passive state (i.e., a state diagonal in the Fock basis with eigenvalues decreasing as the energy increases) majorizes the Husimi Q representation of any other one-mode state with the same spectrum, i.e., it maximizes any convex functional.
KW - Husimi Q representation
KW - Quantum Gaussian states
KW - Schatten norms
KW - Von Neumann entropy
KW - Wehrl entropy
UR - http://www.scopus.com/inward/record.url?scp=85028983061&partnerID=8YFLogxK
U2 - 10.1007/s11005-017-0994-3
DO - 10.1007/s11005-017-0994-3
M3 - Journal article
AN - SCOPUS:85028983061
VL - 108
SP - 97
EP - 116
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
IS - 1
ER -
ID: 189701371