Related papers: Wigner entropy conjecture and the interference for…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
CConsider a bipartite quantum system consisting of two subsystems A and B. The reduced density matrix ofA a is obtained by taking the partial trace with respect to B. In this work, we will show that the Wigner distribution of this reduced…
In a recent paper, Tilma, Everitt {\it et al.} derived a generalized Wigner function that can characterize both the discrete and continuous variable states, i.e., hybrid states. As such, one can expect that the negativity of the generalized…
I show that a nonnegative Wigner function that represents a mixture of Fock states is majorized by the Wigner function of the vacuum state. As a consequence, the integration of any concave function over the Wigner phase space has a lower…
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic…
We propose an experiment demonstrating the nonlocality of a quantum singlet-like state generated from a single photon incident on a beam splitter. Each of the two spatially separated apparatuses in the setup performs a strongly unbalanced…
We generalize the concept of the Wehrl entropy of quantum states which gives a basis-independent measure of their localization in phase space. We discuss the minimal values and the typical values of these R{enyi-Wehrl entropies for pure…
In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent…
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…
We develop a complex-entropy framework for Wigner negativity and apply it to avoided crossings in an oval quantum billiard. For a real Wigner function the Gibbs--Shannon functional becomes complex; its imaginary part, proportional to the…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
Recent experimental results demonstrated the generation of a quantum superpositon (MQS), involving a number of photons in excess of 5x10^4, which showed a high resilience to losses. In order to perform a complete analysis on the effects of…
Given a choice of an ordered, orthonormal basis for a $D$-dimensional Hilbert space, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents any quantum state as a real, normalized…
In every state of a quantum particle, Wigner's quasidistribution is the unique quasidistribution on the phase space with the correct marginal distributions for position, momentum, and all their linear combinations.