Related papers: Interference in discrete Wigner functions
A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($\chi^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are…
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
A one-parameter generalized Wigner-Heisenberg algebra( WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule $[\hat{x}, \hat{p}_{\lambda}] = i(1 + 2\lambda \hat{R})$ and also highlights the dynamical…
We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results…
Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays everywhere positive, which obscures such purely quantum phenomena as non-locality and entanglement. With the advent of the electron microscopes…
The use of special quantum states to achieve sensitivities below the limits established by classically behaving states has enjoyed immense success since its inception. In bosonic interferometers, squeezed states, number states and cat…
A superconducting qubit coupled to a microwave resonator provides a controllable system that enables fundamental studies of light-matter interactions. In the dispersive regime, photons in the resonator exhibit induced frequency and phase…
We introduce a framework for implementing quantum operations as steady states of a subsystem in an extended Hilbert space. Each operation has a spectral criterion for reaching the steady state. This adds a `spectral switch' mechanism to the…
We study a qubit-oscillator system, with a time-dependent coupling coefficient, and present a scheme for generating entangled Schr\"odinger-cat states with large mean photon numbers and also a scheme that protects the cat states against…
The usual position-momentum commutation relation plays a fundamental role in the mathematical description of continuous-variable quantum systems. In the case of a qudit described by a Hilbert space of a high enough dimension, there exists a…
Quantum superpositions of macroscopically distinct classical states, so-called Schr\"{o}dinger cat states, are a resource for quantum metrology, quantum communication, and quantum computation. In particular, the superpositions of two…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate…
We investigate the utility of non classical states of simple harmonic oscillators (a superposition of coherent states) for sensitive force detection. We find that like squeezed states a superposition of coherent states allows the detection…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary…
The evolution of the Schr\"{o}dinger-cat states in a dissipative parametric amplifier is examined. The main tool in the analysis is the normally ordered characteristic function. Squeezing, photon-number distribution and reduced factorial…