Related papers: Local sampling of the SU(1,1) Wigner function
In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern…
This paper contains a brief sketch of some methods that can be used to obtain the Wigner function for a number of systems. We give an overview of the technique as it is applied to some simple differential systems related to diffusion…
We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular…
We report a direct measurement of the Wigner function characterizing the quantum state of a light mode. The experimental scheme is based on the representation of the Wigner function as an expectation value of a displaced photon number…
We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator…
We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group…
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which…
The effects of the spatiotemporal degrees of freedom on the practical implementation of an SU(1,1) interferometry is investigated. A recently developed Wigner functional approach is used to obtain the phase sensitivity of such an SU(1,1)…
We present a new operator method in the Heisenberg representation to obtain the signal of parity measurement within a lossless SU(1,1) interferometer. Based on this method, it is convenient to derive the parity signal directly in terms of…
Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for…
The recently proposed scheme for direct sampling of the quantum phase space by photon counting is discussed within the Wigner function formalism.
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
We extend shapelets for the analysis of galaxy images to be available in a phase space, introducing \textit{Wigner Function Shapelets (WFS)}. Whereas conventional shapelets expand images separately in configuration or Fourier space using…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We propose a very simple experimental setup to measure, via photon counting, the overlap of the Wigner functions characterizing two single mode light beams. We show that this scheme can be applied to determine directly the phase space…
The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
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…
In this work we study symplectic unitary representations for the Galilei group. As a consequence a Non-Linear Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…