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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…

Nonclassicality cannot be a single-observable property since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior from the joint measurement of…

The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…

We investigate the utility of non classical states of simple harmonic oscillators (a superposition of coherent states) for sensitive force detection. We find that like squeezed states a superposition of coherent states allows the detection…

A bipartite quantum state is tomographically faithful when it can be used as an input of a quantum operation acting on one of the two quantum systems, such that the joint output state carries a complete information about the operation…

The classicality of the Gamma Model, an analytically solvable quantum oscillator with non-linear dynamics, is investigated using the overlap dynamics, also known as the Loschmidt Echo, and roughness, a classicality measure based on the…

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…

The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…

The quantum speed limit and the Wigner function of open system models are studied. To this end, we use the phase covariant and a two-qubit model interacting with a squeezed thermal bath via position-dependent coupling. The dependence of the…

Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…

We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and…

Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…

Propagating modes of light with negative-valued Wigner distributions are of fundamental interest in quantum optics and represent a key resource in the pursuit of optics-based quantum information technologies. Most schemes proposed or…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

Gaussian quantum states hold special importance in the continuous variable (CV) regime. In quantum information science, the understanding and characterization of central resources such as entanglement may strongly rely on the knowledge of…

We derive a compact expression for the second-order correlation function $g^{(2)} (0)$ of a quantum state in terms of its Wigner function, thereby establishing a direct link between $g^{(2)} (0)$ and the state's shape in phase space. We…

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing…

The aim of this work is to estimate a quadratic functional of a unknown Wigner function from noisy tomographic data. The Wigner function can be seen as the representation of the quantum state of a light beam. The estimation of a quadratic…

Motivated by quantum experiments with nanomechanical systems, the evolution of a Kerr oscillator with focus on creation of states with a negative Wigner function is investigated. Using the phase space formalism, results are presented that…

This article contains a review of an alternative theory of squeezing, based entirely on the wave function description of the squeezed states. Quantum field theoretic approach is used to describe the squeezing of the electromagnetic field in…