Phase space distributions in information theory

Abstract

We use phase space distributions specifically, the Wigner distribution (WD) and Husimi distribution (HD) to investigate certain information-theoretic measures as descriptors for a given system. We extensively investigate and analyze Shannon, Wehrl and Renyi entropies, its divergences, mutual information and other correlation measures within the context of these phase space distributions. The analysis is illustrated with an anharmonic oscillator and is studied with respect to perturbation parameter ($\lambda$) and states ($n$). The entropies associated with the Wigner distribution are observed to be lower than those of the Husimi distribution, which aligns with the findings regarding the marginals. Moreover, the real components of the entropies associated with the Wigner distribution tend to approach the entropic uncertainty bound more closely compared to those of the corresponding Husimi distribution. Moreover, we quantify the precise amount of information lost when opting for the Husimi distribution over the Wigner distribution for characterizing the specified system. Since it is not always positive definite, the entropies cannot always be defined.

References in corpus (32)

• Estimating Mutual Information
• Entanglement Entropy and Quantum Field Theory
• Rényi Divergence and Kullback-Leibler Divergence
• Measuring entanglement entropy through the interference of quantum many-body twins
• Negativity of the Wigner function as an indicator of nonclassicality
• On quantum Renyi entropies: a new generalization and some properties
• Probing entanglement entropy via randomized measurements
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Quark Wigner Distributions and Orbital Angular Momentum
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Information Entropy, Information Distances and Complexity in Atoms
• A Characterization of Entropy in Terms of Information Loss
• The Cauchy-Schwarz divergence for Poisson point processes
• Fisher's information for the position-dependent mass Schrödinger system
• Shannon Information Entropy in Position Space for Two-Electron Atomic Systems
• Continuous-variable entropic uncertainty relations
• Quantum information entropies of the eigenstates and the coherent state of the Pöschl-Teller potential
• The structure of Renyi entropic inequalities
• Quark Wigner Distributions and Orbital Angular Momentum in Light-front Dressed Quark Model
• On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles
• Wigner Distributions for Gluons in Light-front Dressed Quark Model
• Entanglement Rényi $\alpha$-entropy
• Information entropic measures of a quantum harmonic oscillator in symmetric and asymmetric confinement within an impenetrable box
• Wehrl entropy, entropic uncertainty relations and entanglement
• Escort--Husimi distributions, Fisher information and nonextensivity
• Quantitative tomography for continuous variable quantum systems
• Quark generalized TMDs at skewness and Wigner Distribution in boost invariant longitudinal space
• Generalized Husimi Functions: Analyticity and Information Content
• Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions
• Experimental Demonstration of Negative-Valued Polarization Quasi-Probability Distribution
• Wigner distribution of Sine Gordon and Kink solitons
• Gluon Generalized TMDs and Wigner Distributions in boost invariant longitudinal space

Cited by in corpus (1)

• Probing information theoretic measures of nonlinear ultracold quantum gases using phase-space distributions