Related papers: Wigner entropy conjecture and the interference for…
Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum…
Wigner's friend experiment and its modern extensions display the ambiguity of the quantum mechanical description regarding the assignment of quantum states. While the friend applies the state-update rule to the system upon observing an…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and show that the continuous version of majorization theory provides an elegant and…
We study degenerate three photon down conversion as a potential scheme for generating nonclassical states of light which exhibit clear signatures of phase space interference. The Wigner function representing these states contains an…
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among…
While commonly used entanglement criteria for continuous variable systems are based on quadrature measurements, here we study entanglement detection from measurements of the Wigner function. These are routinely performed in platforms such…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…
Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…
According to Wigner theorem, transformations of quantum states which preserve the probabilities are either unitary or antiunitary. This short communication presents an elementary proof of this theorem that significantly departs from the…
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…
We consider a quantity that is the differential relative entropy between a generic Wigner function and a Gaussian one. We prove that said quantity is minimized with respect to its Gaussian argument, if both Wigner functions in the argument…
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
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…
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale, which are crucial in determining the sensitivity of these states to phase-space…
States with a negative Wigner function, a significant subclass of nonclassical states, serve as a valuable resource for various quantum information processing tasks. Here, we provide a criterion for detecting such quantum states…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
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…
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…