相关论文: Moments of the Wigner Distribution and a Generaliz…

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…

We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the…

The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…

We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner…

We consider the problem of setting up the Wigner distribution for states of a quantum system whose configuration space is a Lie group. The basic properties of Wigner distributions in the familiar Cartesian case are systematically…

Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…

We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…

We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…

We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help…

This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The…

We study a generalization of the Wigner function to arbitrary tuples of hermitian operators. We show that for any collection of hermitian operators A1...An , and any quantum state there is a unique joint distribution on R^n, with the…

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…

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…

The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…

It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…

Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…

In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…

We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…

Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous…