Negativity of the Wigner function is arguably one most striking non-classical features quantum states. Beyond its fundamental relevance, it also a necessary resource for speedup with continuous variables. As technologies emerge, need to identify and characterize resources which provide an advantage over existing classical becomes more pressing. Here we derive witnesses negativity single mode mu...

We define the Wigner entropy of a quantum state as differential Shannon function state. This quantity is properly defined only for states that possess positive function, which we name Wigner-positive states, but argue it proper measure uncertainty in phase space. It invariant under symplectic transformations (displacements, rotations, and squeezing) conjecture lower bounded by $ln\ensuremath{\p...

Applying the fractional Fourier transform (FRFT) and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the n-dimensional Wigner distribut...

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have propo...

We introduce a τ -dependent Wigner representation, Wigτ , τ ∈ [0, 1], which permits us to define a general theory connecting time-frequency representations on one side and pseudo-differential operators on the other. The scheme includes various types of time-frequency representations, among the others the classical Wigner and Rihaczek representations and the most common classes of pseudo-differe...

The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mod...

A conditional kinetic energy is defined in terms of the Wigner distribution. It is shown that this kinetic energy may become negative for negative Wigner distributions. A free particle wave packet with negative kinetic energy will spread in a nonclassical manner. 1 The Free Particle In classical statistical mechanics, a particle is described in terms of a nonnegative phase space distribution P ...