Related papers: Operator Space theory: a natural framework for Bel…
From the beginning of quantum mechanics, there has been a discussion about the concept of reality, as exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell…
Based on local unitary operators acting on a n-dimensional Hilbert-space, we investigate selective and collective operator basis sets for N-particle quantum networks. Selective cluster operators are used to derive the properties of general…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We investigate the maximal violation of Bell inequalities for two $d$-dimensional systems by using the method of Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors…
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
Steerability is a characteristic nonlocal trait of quantum states lying in between entanglement and Bell nonlocality. A given quantum state is considered to be steerable if it violates a suitably chosen steering inequality. A quantum state…
We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger…
We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out,…
In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the…
Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We consider a subclass of bipartite CHSH-type Bell inequalities. We investigate operations, which leave their Tsirelson bound invariant, but change their classical bound. The optimal observables are unaffected except for a relative rotation…
In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general…
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing…
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…
Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality…