Related papers: Continuous-Variable Bell Inequalities in Phase Spa…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
Introducing asymmetry into the Weyl representation of operators leads to a variety of phase space representations and new symbols. Specific generalizations of the Husimi and the Glauber-Sudarshan symbols are explicitly derived
The phase space $S\times Z$ for a particle on a circle is considered. Displacement operators in this phase space are introduced and their properties are studied. Wigner and Weyl functions in this context are also considered and their…
We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter 0<p<1. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation…
It is shown that Bell's proof of violation of local realism in phase space is incorrect. Using Bell's approach, a violation can be derived also for nonnegative Wigner distributions. The error is found to lie in the use of an unnormalizable…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible…
We present an experimental investigation of two-photon interference using a continuous-wave laser. We demonstrate the violation of the CHSH inequality using the phase randomized weak coherent states from a continuous wave laser. Our…
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…
The classical limit of the Wigner-Weyl representation is used to approximate products of bound-continuum matrix elements that are fundamental to many coherent control computations. The range of utility of the method is quantified through an…
A concise and self-contained introduction to the Bell inequality in relativistic Quantum Field Theory is presented. Taking the example of a real scalar massive field, the violation of the Bell inequality in the vacuum state and for causal…
We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spin- like systems, which is the case when…
The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is…
The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…
It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…
We study the Weyl-Wigner transform in the case of discrete variables defined in a Hilbert space of finite prime-number dimensionality $N$. We define a family of Weyl-Wigner transforms as function of a phase parameter. We show that it is…
The consistency test and error estimation for the data concerning recently reported violation of Bell inequality for Josephson phase qubits are presented in details. It is pointed out that the deviation of the Bell signal from the classical…
We describe a new Bell test for two-particle entangled systems that engages an unbounded continuous variable. The continuous variable state is allowed to be arbitrary and inaccessible to direct measurements. A systematic method is…
We present a formulation of the Bell inequalities using simple correlated photon number states and phase measurements. Such tests generally require binning of the information, and this effect is closely examined. Our proposal opens up the…
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A…