Related papers: Discrete Wigner Functions from Informationally Com…
The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics…
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…
In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum…
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…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
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…
Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the…
The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their $d^2$-outcomes are enough to reconstruct any $d$-dimensional quantum state.…
We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of…
The Wigner Phase Operator (WPO) is identified as an operator valued measure (OVM) and its eigen states are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
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…
Polarization quasiprobability distribution defined in the Stokes space shares many important properties with the Wigner function for the position and momentum. Most notably, they both give correct one-dimensional marginal probability…
Wigner functions are broadly used to probe non-classical effects in the macroscopic world. Here we develop an orbital-free functional framework to compute the 1-body Wigner quasi-probability for both fermionic and bosonic systems. Since the…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…