The Bell inequalities and their irrelevance to the problem of locality in quantum mechanics

A straightforward derivation of the Bell inequalities is given, without in any way appealing to locality. This demonstrates the incompatibility of both local and nonlocal hidden variables theories with quantum mechanics, and the irrelevance of the Bell inequalities to the problem of (non)locality in such theories.     

Geometro-stochastic locality in quantum spacetime and quantum diffusions

The issue of the intrinsic nonlocality of quantum mechanics raised by J. S. Bell is examined from the point of view of the recently developed method of geometro-stochastic quantization and its applications to general relativistic quantum theory. This analysis reveals that a distinction should be made between the topological concept of locality used in formulating relativistic causality and a type of geometric locality based on the concept of fiber bundle, which can be used in extending the strong equivalence principle to the quantum domain. Both play an essential role in formulating a notion of geometro-stochastic propagation based on quantum diffusions, which throws new light on the EPR paradox, on the origin of the arrow of time, and on other fundamental issues in quantum cosmology and the theory of measurement.     

On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

On the relevance of the bell inequalities to the problem of locality in quantum mechanics

A recent claim by De Muynck that the Bell inequalities are completely irrelevant to the locality problem is opposed. The various ways in which the inequalities are relevant and not relevant are briefly discussed.     

General quantum field theories and strict locality

A class of general quantum field theories without explicit use of fieldsA(x) is defined by a set of postulates for the von Neumann algebras ? _C of local observables. The vacuum state is cyclic with respect to any ? _C , and the Borchers tube theorem is shown to hold. Some ? _C are factors and not of finite type. A property of local observables called strict locality is formulated and expressed by means of a necessary and sufficient condition for the algebras ? _C . It is proved for finite regions.     

Quantum erasure and the locality problem

The problem of locality arising in connection with the quantum-erasure experiments is considered using the algebraic approach. We demonstrate that, contrary to a widespread opinion, the results of these experiments can be reconciled with the existence of a local physical reality determining the results of local measurements. A clear physical interpretation of the quantum-erasure experiments, that is consistent with the classical concepts, is given.     

Approximate locality for quantum systems on graphs

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)]: we show that if U is a sparse unitary operator with a gap Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Delta increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.     

The quantum cocktail party problem

正The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party [1].This selective attention problem was firstly defined as the"cocktail party problem"(CPP) by Cherry [2]in 1953.In recent years,machine-learning based approaches to solve the CPP were essential for many industrial applications such as automated speech recognition.The independent component analysis (ICA) is such an algorithm particularly     

The quantum cocktail party problem

The cocktail party problem is a selective attention problem in classical information processing,which has been extensively studied in computer science and neuroscience for decades.It considers the scenario in which signals are emitted from several different independent sources,and detectors detect different mixings of these signals,and target the recovery of individual sources from the information of detectors,regardless of how these signals are mixed as a prior.     

On stochastic Einstein locality in algebraic relativistic quantum field theory

This paper assesses Miklós Rédei's [1991] proof of the proposition that algebraic relativistic quantum field theory is stochastic Einstein local. The conclusion is that either Rédei's proof is spurious, in that it does not really prove what it intends to establish, or that the proof is fallacious. The paper is self-contained in the sense that the few ingredients of algebraic quantum theory that go into Rédei's proof are first summed up. Then Hellman's definition of stochastic Einstein locality is discussed, a detailed exposition is offered of Rédei's proof, and finally the author's refutation is explicated.     

The scattering problem in quantum mechanics as an eigenvalue problem

A method is proposed which allows the scattering problem to reduce to the eigenvalue problem. Unlike the usual method when the scattering phase is extracted from the asymptotics of solution of the Cauchy problem at a given collision energy, in the proposed method the collision energy is obtained from the solution of the Sturm-Liouville problem at a given scattering phase. The continuous analog of the Newton method is used for the numerical realization of the proposed method.     

The computer-based model of quantum measurements

Physics of Atomic Nuclei - Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic...     

The problem of objectification in quantum mechanics

The hypotheses of weak and strong objectification of quantum mechanical observables, as well as theoretical arguments and experimental evidence against these hypotheses, are systematically reviewed.     

Violations of locality in correlation measurements with a beam splitter

It is pointed out that the locality violations that are expected to show up in the polarization correlation experiments recently discussed by Chubarov and Nikolayev, should be readily observable with the poissonian photon pairs produced in down conversion.     

On quantum measurements

Is the reduction of the wavefunction a real physical process? A mental experiment providing an answer to this question is considered.     

Nonideal quantum measurements

A partial ordering in the class of observables ( positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter definition, be justified operationally. The nonideality notion is compared to other quantum estimation theoretic methods. Measures for the amount of nonideality are derived from information theory.     

The problem of decay in nonrelativistic quantum mechanics

In this paper the time-dependent Schrödinger equation with an arbitrary potential with finite effective radius is solved. Outside the effective radius of the potential a universal solution is obtained which does not depend on the initial state and which describes the evolution of a resonance state. In the single-resonance approximation various space-time domains are studied in which an exponential decay law can be observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 38–43, December, 1972.     

On measurements in quantum mechanics

It is shown that measurements of quantum variables can be understood on the basis of the time-dependent Schroedinger equation, without assuming any “jump” os “reduction of wave packets”. The reduction of the wave packets is admissible and giver correct results, but it is not necessary.