Related papers: Probabilistic Q-function distributions in fermioni…
We introduce a certain discrete probability distribution $P_{n,m,k,l;q}$ having non-negative integer parameters $n,m,k,l$ and quantum parameter $q$ which arises from a zonal spherical function of the Grassmannian over the finite field…
We determine the inner product on the Hilbert space of wavefunctions of the universe by imposing the Hermiticity of the quantum Hamiltonian in the context of the minisuperspace model. The corresponding quantum probability density reproduces…
We put forward several information-theoretic measures for analyzing the uncertainty of fermionic phase-space distributions using the theory of supernumbers. In contrast to the bosonic case, the anticommuting nature of Grassmann variables…
The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…
Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…
A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process.…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
The $q$-deformed statistics for fermions arising within the non-extensive thermostatistical formalism has been applied to the study of various quantum many-body systems recently. The aim of the present note is to point out some subtle…
We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…