Formal relation between Pegg-Barnett and Paul quantum phase frameworks

Abstract

The problem of defining a hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we make an explicit connection between two of the most prominent approaches, by proving that the probability distribution of phase in the Paul formalism follows exactly from the Pegg-Barnett formalism by combining the latter with the quantum limited amplifier channel. Our findings suggest that the Paul framework may be viewed as a semi-classical limit of the Pegg-Barnett approach.

8 pages + 2-page Appendix

References in corpus (9)

• Generating random density matrices
• Number-phase entropic squeezing and nonclassical properties of a three-level atom interacting with a two-mode field: Intensity-dependent coupling, deformed Kerr medium and detuning effects
• Single- and two-mode quantumness at a beam splitter
• Quantum phase properties of photon added and subtracted displaced Fock states
• Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state
• Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach
• The Pegg-Barnett Formalism and Covariant Phase Observables
• The Wehrl entropy has Gaussian optimizers
• The Pegg-Barnett phase operator and the discrete Fourier transform

Cited by in corpus (3)

• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• Classicality of the Bogoliubov transformations and the dynamical Casimir effect through the reduced state of the field
• Husimi phase distribution in non-Gaussian operations