2014
DOI: 10.1016/j.aop.2014.10.011
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From the Weyl quantization of a particle on the circle to number–phase Wigner functions

Abstract: a b s t r a c tA generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number-phase Wigner function in quantum optics. A Wigner function for the stateρ and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner functions are considered.

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Cited by 13 publications
(20 citation statements)
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“…with f given by (1.8). As it has been pointed out by many authors [2][3][4][5][6] the formula (1.11) gives the expectation value for the quantum phase-function f (φ) equal to the one calculated within the Pegg-Barnett approach to quantum phase [7][8][9]. Consequently, our choice for a number-phase Wigner function (1.4) seems to be appropriate when the Pegg-Barnett formulation is considered.…”
Section: Introductionmentioning
confidence: 87%
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“…with f given by (1.8). As it has been pointed out by many authors [2][3][4][5][6] the formula (1.11) gives the expectation value for the quantum phase-function f (φ) equal to the one calculated within the Pegg-Barnett approach to quantum phase [7][8][9]. Consequently, our choice for a number-phase Wigner function (1.4) seems to be appropriate when the Pegg-Barnett formulation is considered.…”
Section: Introductionmentioning
confidence: 87%
“…In recent works [1][2][3] we have developed a theory of quantum phase which is based on some enlarging of the Fock space to the Hilbert space of the square integrable functions on the circle, L 2 (S 1 ). Then the well known machinery of the Naimark projection is employed to find the respective objects in the original Fock space.…”
Section: Introductionmentioning
confidence: 99%
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“…Thus, we usually assume the classical phase space to be also the quantum one. We are also aware of exceptions, like sets whose classical phase space is a cylinder A detailed analysis of this situation can be found in [ 44 , 45 , 46 , 47 ].…”
Section: The Structure Of Quantum Phase Spacementioning
confidence: 99%