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.

The Wehrl entropy has Gaussian optimizers

De Palma, Giacomo
2018

Abstract

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.
2018
Settore MAT/07 - Fisica Matematica
Wehrl entropy; Von Neumann entropy; Husimi Q representation; Quantum Gaussian states; Schatten norms
File in questo prodotto:
File Dimensione Formato  
The Wehrl entropy has Gaussian optimizers.pdf

Open Access dal 10/09/2018

Tipologia: Accepted version (post-print)
Licenza: Solo Lettura
Dimensione 248.64 kB
Formato Adobe PDF
248.64 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/68991
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 18
  • OpenAlex ND
social impact