Related papers: Permutation Symmetry Determines the Discrete Wigne…
A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require…
We construct, using simple geometrical arguments, a Wigner function defined on a discrete phase space of arbitrary integer Hilbert-space dimension that is free of redundancies. ``Ghost images'' plaguing other Wigner functions for discrete…
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…
We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-$\tfrac{1}{2}$ systems. We develop a…
We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem…
The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an…
The Gottesman-Knill theorem established that stabilizer states and operations can be efficiently simulated classically. For qudits with dimension three and greater, stabilizer states and Clifford operations have been found to correspond to…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…
Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set L of all 1-dimensional subspaces of a…
Quantum information is a common topic of research in many areas of quantum physics, such as quantum communication and quantum computation, as well as quantum thermodynamics. It can be encoded in discrete or continuous variable systems, with…
We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a…
A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a unitary transformation, or an antiunitary…
We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…
In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary…
We report a direct measurement of the Wigner function characterizing the quantum state of a light mode. The experimental scheme is based on the representation of the Wigner function as an expectation value of a displaced photon number…
A class of signed joint probability measures for n arbitrary quantum observables is derived and studied based on quasi-characteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner…
We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a…