Related papers: Quantum expectations via spectrograms
We introduce a new density for the representation of quantum states on phase space. It is constructed as a weighted difference of two smooth probability densities using the Husimi function and first-order Hermite spectrograms. In contrast…
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…
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…
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…
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 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…
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…
A new mathematical and computational technique for calculating quantum vacuum expectation values of energy and momentum densities associated with electromagnetic fields in bounded domains containing inhomogeneous media is discussed. This…
Quantum gas microscopes offer unprecedented insights into quantum many-body states of cold atomic gases. Here we introduce concrete protocols for extending quantum gas microscopes to measure in phase space, by mapping momentum onto…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
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.…
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
Introduction Phase space methods in quantum mechanics - The Wigner function - The Husimi function - Inverse participation ratio Anderson model in phase space - Husimi functions - Inverse participation ratios
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
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…
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…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…