Related papers: A new Phase Space Density for Quantum Expectations
We discuss a new phase space method for the computation of quantum expectation values in the high frequency regime. Instead of representing a wavefunction by its Wigner function, which typically attains negative values, we define a new…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
This paper proposes an approach to interpreting quantum expectation values that may help address the quantum measurement problem. Quantum expectation values are usually calculated via Hilbert space inner products and, thereby, differently…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
We analyse the dynamics of expectation values of quantum observables for the time-dependent semiclassical Schr\"odinger equation. To benefit from the positivity of Husimi functions, we switch between observables obtained from Weyl and…
The concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…
Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides…
The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the two-dimensional $U(3)$ vibron model for $N$-size molecules. We show that the inverse participation ratio and Wehrl's entropy of the Husimi…
We develop the Husimi map for visualizing quantum wavefunctions using coherent states as a measurement of the local phase space to produce a vector field related to the probability flux. Adapted from the Husimi projection, the Husimi map is…
In this Letter, we interpret the Husimi function as the conditional probability density of continuously measuring a stream of constant position and momentum outcomes, indefinitely. This gives rise to an alternative definition that naturally…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good…
We present efficient circuits that can be used for the phase space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can be…
Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the…
Over decades, the time evolution of Wigner functions along classical Hamiltonian flows has been used for approximating key signatures of molecular quantum systems. Such approximations are for example the Wigner phase space method, the…
In the context of nucleon structure, the Wigner distribution has been commonly used to visualize the phase-space distribution of quarks and gluons inside the nucleon. However, the Wigner distribution does not allow for a probabilistic…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…
We introduce a quantifier of phase-space complexity for discrete-variable (DV) quantum systems. Motivated by a recent framework developed for continuous-variable systems, we construct a complexity measure of quantum states based on the…
In this study, we compare the Wigner function $W$, its modulus, and the Husimi distribution $H$ in a one-dimensional quantum system exhibiting a transition from a single-well to a double-well configuration, using the quasi-exactly solvable…
We are concerned with an information-theoretic measure of uncertainty for quantum systems. Precisely, the Wehrl entropy of the phase-space probability $Q^{(m)}_{\hat{\rho}}=\left\langle z,m|\hat{\rho}|z,m\right\rangle $ which is known as…