Related papers: Bell-CHSH inequality and unitary operators
Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as…
The violation of the Bell-CHSH inequality for bipartite systems is discussed by making use of the pseudospin operators which enable us to group all modes of the Hilbert space of the system in pairs. We point out that a single pair can be…
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have…
There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust.…
We emphasize the difficulties of an experiment that can definitely discriminate between local realistic hidden variables theories and quantum mechanics using the Bell CHSH inequalities and a real measurement apparatus. In particular we…
It is pointed out that the vertex operators of a chiral boson in 1+1 dimensions provide an explicit realization of dichotomic, bounded, Hermitian operators that saturate the Tsirelson bound of the Bell-CHSH inequality in the vacuum state.
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
Bell-CHSH-like inequalities have been very successful in benchmarking {\it spatial} quantum correlations. However, as this paper illustrates, they are in general not sufficient for benchmarking {\it temporal} quantum correlations. To show…
We show that classical processes corresponding to operators what satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell's inequality for their covariances can be extended…
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
The interaction between Unruh-De Witt spin $1/2$ detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory…
The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner…
Use of the vacuum projector and of the unitary displacement operators enables us to construct Hermitian dichotomic operators. These operators are employed to scrutinize the violation of the Bell-CHSH inequality for entangled coherent…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although…
The use of the vacuum projector $|0 \rangle \langle 0| $ and of the unitary Weyl operators enables us to construct a set of Hermitian dichotomic operators in relativistic scalar Quantum Field Theory in Minkowski spacetime. Employing test…
A generalization of the CHSH-Bell inequality to arbitrary many settings is presented. The singlet state of two spin $\half$ violates this inequality for all numbers of setting. In the limit of arbitrarily large number of settings, the…
By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a $2\otimes2$ subspace. We find that, for infinite-dimensional systems, the corresponding…
It is well-known that the set of statistics that can be observed in a Bell-type experiment is limited by quantum theory. Unfortunately, tools are missing to identify the precise boundary of this set. Here, we propose to study the set of…
Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of $S_4$ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.