Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

Wigner function of the thermo number states

Based on thermo field dynamics (TFD) and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature (named thermo number states). The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.     

The Wigner function in the relativistic quantum mechanics

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.     

Quantum phase distribution and the number—phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states:solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.     

Numerical representation of quantum states in the positive-P and Wigner representations

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many-body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose–Einstein condensates, and give some examples of how this can be done.     

A quasi-classical formulation of the Wigner function approach to quantum ballistic transport

The time evolution of Wigner's function is shown to be a linear superposition of classical distributions unfolded by a family of classical hamiltonians.     

Wigner distribution function expression for the tunnelling time in quantum resonant structures

A definition of the tunnelling time in terms of the Wigner distribution function is proposed, which is shown to be identical to the expression for the tunnelling time derived in the group velocity approach.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient α, it can generate a variety of nonclassical states.     

Wigner dynamics of quantum semi-relativistic oscillator

The integral Wigner–Liouville equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected ‘protuberances’ in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.     

Wigner function and the parity operator

It is shown that the linear canonical transformation properties of the Wigner function P(q, p) naturally require it to be proportional to the expectation value of the parity operator that performs reflections about the phase-space point (q, p).     

Wigner functions and quantum interference in optics

A new, approximate generalized Wigner function based on discrete coherent state superpositions is introduced. It is shown that in contrast to the exact generalized Wigner function that may not exist in some region of its parameter the proposed approximate function exists everywhere.