We consider the problem of high-frequency asymptotics for the time-dependent onedimensional Schrödinger equation with rapidly oscillating initial data. This problem is commonly studied via the WKB method. An alternative method is based on the limit Wigner measure. This approach recovers geometrical optics, but, like the WKB method, it fails at caustics. To remedy this deficiency we employ the s...

The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is applied as well to seek indications of specific quantum properties of quantum systems leading to impossibility of the classical approximation construction. Mos...

We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the telepor-tation protocol. In addition within the framework of the Wigner-function formalism all the imperfections of the manipulations can be easily taken into account. All quantum mechanical ph...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete phase-space, i.e. on a finite discrete square grid. These discrete Wigner functions possess a number of properties similar to the Wigner function for a continuous quant...

We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the telepor-tation protocol. In addition within the framework of the Wigner-function formalism all the imperfections of the manipulations can be easily taken into account. All quantum mechanical ph...

We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the telepor-tation protocol. In addition within the framework of the Wigner-function formalism all the imperfections of the manipulations can be easily taken into account. All quantum mechanical ph...

In the beginning of the 1950’s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the socalled Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. ...