Generalized<i>SU</i>(2) covariant Wigner functions and some of their applications

Klimov, A. B.; Romero, José Luis; Guise, Hubert de

doi:10.1088/1751-8121/50/32/323001

Cited by 52 publications

(59 citation statements)

References 165 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also think that similar features hold far beyond the two elementary symmetries which have been examined here. There exist many versions of the Wigner function or equivalent quasi-distribution for other groups, see for instance [ 39 , 40 ] for SU

and references therein. In the case of non-compact groups, particularly those which are semi-direct products of groups, the existence of square-integrability of the UIR requested by the resolution of the identity lying at the heart of the construction is in general not guaranteed.…”

Section: Discussionmentioning

confidence: 99%

Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Bergeron

Gazeau

2018

Entropy

View full text Add to dashboard Cite

Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all resources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. We first review this quantization scheme before revisiting the cases where symmetry covariance is described by the Weyl-Heisenberg group and the affine group respectively, and we emphasize the fundamental role played by Fourier transform in both cases. As an original outcome of our generalisations of the Wigner-Weyl transform, we show that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

show abstract

Section: Discussionmentioning

confidence: 99%

Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Bergeron

Gazeau

2018

Entropy

View full text Add to dashboard Cite

show abstract

“…The exact evolution equation for W (s) ρ (Ω) has been derived in [59] (see also [60] and [61], where the corresponding starproduct for the map is discussed). In most physical applications only Hamiltonians quadratic in the spin generators play an important role.…”

Section: Hamiltonian Dynamics and Currents On The Spherementioning

confidence: 99%

Quasiprobability currents on the sphere

et al. 2020

View full text Add to dashboard Cite

We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.

show abstract

“…The representation of Kraus operators E a i for this channel [25] is given by, According to Eqs. (5), (11)and (7), the final output state that passes through C bf is given by,…”

Section: The Bit Flip Channel C Bfmentioning

confidence: 99%

“…[5] investigated analytically the Wigner function distribution of a two-qubit field system in the presence of pure phase noisy. The s-parameterized Q − P D is described in the angular momentum basis via atomic coherent state [6,7]. However, the value of s-parameters determines the type of the Q − P D, where s = −1, 0, 1, represent the Husimi-Berezin Q-function, [8,9], Wigner quasi-distribution function [10,11], and the P -function [12], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…where r is the acceleration such that, tan r = exp(−πωc/a), 0 ≤ r ≤ π/4, −∞ ≤ a ≤ ∞, c is the speed of light, and ω is the frequency. Due to the transformation (7), the space is splitting into two regions, I and II. By tracing out over all the degrees of freedom on the second region II, the final state which describes the accelerated system,ρ acc a,b is given by,…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Wigner function of noisy accelerated two-qubit system

Abd‐Rabbou

Metwally

Ahmed

et al. 2019

Quantum Inf Process

View full text Add to dashboard Cite

In this manuscript, the behavior of the Wigner function of accelerated and non-accelerated two qubit system passing through different noisy channels is discussed. The decoherence of the initial quantum correlation due to the noisy channels and the acceleration process is investigated by means of Wigner function. The negative (positive) behavior of the Wigner function predicts the gain of the quantum (classical) correlations. Based on the upper and lower bounds of the Wigner function, the entangled initial state loses its quantum correlation due the acceleration process and the strengths of the noisy channels. However, by controlling the distribution angles, the decoherence of these quantum correlation may be suppressed. For accelerated state, the robustness of the quantum correlations contained in the initial state appears in different ranges of the distribution angles depending on the noisy type. For the bit phase flip and the phase flip channels, the robustness of the quantum correlations is shown at any acceleration and large range of distribution angles. However, the fragility of the quantum correlation is depicted for large values for strength of the bit flip channel. Different profiles of the Wigner function are exhibited for the quantum and classical correlations, cup, lune, hemisphere.

show abstract

GeneralizedSU(2) covariant Wigner functions and some of their applications

Abstract: We survey some applications of SU(2) covariant maps to the phase space quantum mechanics of systems with fixed or variable spin. A generalization to SU(3) symmetry is also briefly discussed in framework of the axiomatic Stratonovich-Weyl formulation.

Cited by 52 publications

References 165 publications

Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

Quasiprobability currents on the sphere

Wigner function of noisy accelerated two-qubit system

Contact Info

Product

Resources

About