Related papers: Gaussian Distributions and Phase Space Weyl--Heise…
We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…
We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…
Mutual space-frequency distribution is proposed and it is shown that Wigner and Weyl distribution functions are only particular cases of these distribution. Mutual distribution for Gaussian signal is analytically obtained. The simple…
Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and…
Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving…
The phase-space description of bosonic quantum systems has numerous applications in such fields as quantum optics, trapped ultracold atoms, and transport phenomena. Extension of this description to the case of fermionic systems leads to…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
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…
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
In this thesis we focus on Gaussian quantum metrology in the phase-space formalism and its applications in quantum sensing and the estimation of space-time parameters. We derive new formulae for the optimal estimation of multiple parameters…
Gaussian quantum mechanics is a powerful tool regularly used in quantum optics to model linear and quadratic Hamiltonians efficiently. Recent interest in qubit-CV hybrid models has revealed a simple, yet important gap in our knowledge,…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
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…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…