5 Wigner functional theory

Sibel Başkal, Young S Kim, Marilyn E. Noz

Ivan Hubač, Pavel Neogrády

Size consistency of the Brillouin-Wigner perturbation theory is studied using the Lippmann-Schwinger equation and an exponential ansatz for the wave function. Relation of this theory to the coupled cluster method is studied and a comparison through the effective Hamiltonian method is also provided.

David K. Ferry, Mihail Nedjalkov

David K. Ferry

The Wigner function has been studied for more than eight decades. Historically, it was developed from the Schrodinger wave equation, although it could have been developed on its own right. The use of the Wigner function is particularly important in scattering problems and clearly shows the transition to the classical world. In general, the Wigner function is not a positive definite function. One of the interesting aspects of the Wigner function is the ability to transfer many of the results of classical transport theory into quantum approaches merely by replacing the Boltzmann distribution with the Wigner function. The Wigner function for either of the two oscillators can be found by integrating out the coordinates of the other oscillator. Modern approaches with the Wigner function provide a distinct formulation that is recognized as equivalent to, but is a different alternative to normal operator-based quantum mechanics.

David K. Ferry, Xavier Oriols, Josef Weinbub

Orsolya Kálmán, M. G. Benedict

The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.