Nonlocal information as condition for violations of Bell inequality and information causality

On the basis of local realism theory, nonlocal information is necessary for violation of Bell's inequality. From a theoretical point of view, nonlocal information is essentially the mutual information on distant outcome and measurement setting. In this work we prove that if the measurement is free and unbiased, the mutual information about the distant outcome and setting is both necessary for the violation of Bell's inequality in the case with unbiased marginal probabilities. In the case with biased marginal probabilities, we point out that the mutual information about distant outcome cease to be necessary for violation of Bell's inequality, while the mutual information about distant measurement settings is still required. We also prove that the mutual information about distant measurement settings must be contained in the transmitted messages due to the freedom of measurement choices. Finally we point out that the mutual information about both distant outcome and measurement settings are necessary for a violation of information causality.     

Numerical Simulation of Bell Inequality's Violation Using Optical Transverse Modes in Multimode Waveguides

We numerically demonstrate that ＇mode-entangled states＇ based on the transverse modes of classical optical fields in multimode waveguides violate Bell＇s inequality. Numerically simulating the correlation measurement scheme of Bell＇s inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell＇s inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.     

Experimental falsification of Leggett's nonlocal variable model

Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also, some models based on nonlocal variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In this Letter, we introduce a family of inequalities, which use a finite number of measurement settings, and which therefore allow testing Leggett's nonlocal model versus quantum physics. Our experimental data falsify Leggett's model and are in agreement with quantum predictions.     

Locality and Bell's Theorem

It is shown that the violation of Bell's inequality allowed by quantum mechanics and the related Bell's theorem without inequalities is accounted for by local commutations of operators representing single-particle observables. It is argued that the idea of nonlocal influencing of one particle on another when they are in spacelike separated regions clearly has neither empirical nor theoretical support.     

Bell's theorem and the nature of reality

We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities, and its consequences. We describe the experiment of Aspect, Dalibard, and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory.Dedicated to J. S. Bell on his 60th birthday.     

Nonlocality in Relativistic Dynamics

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.     

Interpretation of the Experiments on Bell's Inequality

The conceptual scheme of the optical polarization experiments on Bell's inequality is discussed. By invoking the distinction between the concepts of state preparation and measumment in quantum mechanics, it is argued that Bell's theorem is not applicable to this class of experiments in the way it is generally done. Consequently, by considering the specific features of the measurements performed hitherto, it is also shown that a local approach can yield the same theoretical prediction as the nonlocal quantum interpretation, even in the absence of other experimental loopholes.     

Uncertain evidence and nonlocality

After the work of Suppes and Zanotti it is clear that the proof of the impossibility of local theories is a probability argument. The notion of locality is essentially a principle of conditional statistical independence which is strictly tied to that of exchangeability. De Finetti's celebrated representation theorem makes the connection clear. The way in which Bell's experiment is performed suggests that the probability function which is more suitable to describe it is not exchangeable, but partially exchangeable. It is known that partially exchangeable probability functions show a nonlocal behavior. Working with these functions, it is possible to make use of observations regarding one stochastic process in order to change the distribution of another process. We enlarge to uncertain evidence a classical probability function we have used in deriving some quantum correlations. By means of this enlargement we give simple examples of a nonlocal probability function.     

On a paradox of probability theory

Costa de Beauregard's proposal concerningretrocausality is formulated in terms of conditional probabilities. In its current formulation his proposal reveals a paradox intrinsic to elementary probability theory. The paradox is perhaps related to the nonlocal causality revealed through Bell's theorem.     

Has quantum nonlocality been experimentally verified?

Bell's theorem tells us that if we wish to preserve the results of quantum theory, then we cannot supplement the theory by any sort of locally determined hidden variables. The Aspect experiments tell us that the results of quantum theory, in certain relevant circumstances, are correct. Thus, some type of information about the result of an experiment must travel to other points of space. If we take a reasonable, simple, model of how a measurement actually produces a result, namely, the GRW collapse model, then the experiments that have so far been done, do not distinguish between instantaneous communication, which is required in the orthodox theory, and communication at the speed of light. We discuss how models which incorporate such communication might be constructed, and urge the need for experimental tests. Likely values of the relevant parameters suggest that these are possible. Finally, we note that, contrary to what is generally claimed, nonlocal collapse models which agree in all circumstances with quantum theory do permit instantaneous signals to be sent over arbitrarily large distances.Text of a talk given at the 1991 Cesena conference,Bell's Theorem and the Foundations of Modern Physics.     

Environment-induced decoherence II. Effect of decoherence on Bell''s inequality for an EPR pair

According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual ‘violation’ of Bell's inequality to a ‘non-violation’ for times larger than a characteristic time scale which is related to the parameters of the fluctuating field. We also look at these inequalities as a function of the spatial separation between the EPR pair.     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.     

Nonlocal interactions: a jammerian analysis

It is general practice to describe a microsystem by means of a model characterized by probability amplitudes possessed at each spacetime point between preparation and measurement events. Recent developments initiated by Bell's theorem indicate that any such model must in some cases be considered as participating in nonlocal interactions. Adapting ideas originated by Jammer, this paper asserts that that conclusion may be indicative only of limitations in the applicability of physical properties in the modelling of microsystems and thus might not lead to inferences about the microsystems in themselves. Recent discussions of the Aharanov-Bohm effect further exemplify the difference in these alternative interpretations of nonlocality.     

Whiteheadian approach to quantum theory and the generalized Bell's theorem

The model of the world proposed by Whitehead provides a natural theoretical framework in which to imbed quantum theory. This model accords with the ontological ideas of Heisenberg, and also with Einstein's view that physical theories should refer nominally to the objective physical situation, rather than our knowledge of that system. Whitehead imposed on his model the relativistic requirement that what happens in any given spacetime region be determined only by what has happened in its absolute past, i.e., in the backward light-cone drawn from that region. This requirement must be modified, for it is inconsistent with the implications of quantum theory expressed by a generalized version of Bell's theorem. Revamping the causal spacetime structure of the Whitehead-Heisenberg ontology to bring it into accord with the generalized Bell's theorem creates the possibility of a nonlocal causal covariant theory that accords with the statistical prediction of quantum theory.Based on lectures given at the University of Texas, March–May 1977. This work was supported in part by the United States Energy Research and Development Agency, in part by the University of Texas, and in part by CERN.     

Existence of “free will” as a problem of physics

The proof of Bell's inequality is based on the assumption that distant observers can freely and independently choose their experiments. As Bell's inequality isexperimentally violated, it appears that distant physical systems may behave as a single, nonlocal, indivisible entity. This apparent contradiction is resolved. It is shown that the free will assumption is, under usual circumstances, an excellent approximation.I have set before you life and death, blessing and cursing: therefore choose life....

相似文献   

Testing locality at colliders via Bell''s inequality?

We consider a measurement of correlated spins at LEP and show that it does not constitute a general test of local-realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can be described by a local hidden variable theory. We conclude that with present experimental techniques it is not possible to test locality via Bell's inequality at a collider experiment. Finally we suggest an improved fixed-target it is not possible to test locality via Bell's inequality at a collider experiment. Finally we suggest an improved fixed-target experiment as a viable test of Bell's inequality.     

Theory of Dynamical Systems and the Relations Between Classical and Quantum Mechanics

We give a review of some works where it is shown that certain quantum-like features are exhibited by classical systems. Two kinds of problems are considered. The first one concerns the specific heat of crystals (the so called Fermi–Pasta–Ulam problem), where a glassy behavior is observed, and the energy distribution is found to be of Planck-like type. The second kind of problems concerns the self-interaction of a charged particle with the electromagnetic field, where an analog of the tunnel effect is proven to exist, and moreover some nonlocal effects are exhibited, leading to a natural hidden variable theory which violates Bell's inequalities.     

An improved Hirota bilinear method and new application for a nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation

The Hirota bilinear method has been studied in a lot of local equations, but there are few of works to solve nonlocal equations by Hirota bilinear method. In this letter, we show that the nonlocal integrable complex modified Korteweg-de Vries (MKdV) equation admits multiple complex soliton solutions. A variety of exact solutions including the single bright soliton solutions and two bright soliton solutions are derived via constructing an improved Hirota bilinear method for nonlocal complex MKdV equation. From the gauge equivalence, we can see the difference between the solution of nonlocal integrable complex MKdV equation and the solution of local complex MKdV equation.     

Multi-place physics and multi-place nonlocal systems

Multi-place nonlocal systems have attracted attention from many scientists. In this paper, we mainly review the recent progresses on two-place nonlocal systems (Alice-Bob systems) and four-place nonlocal models. Multi-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity, time reversal, charge conjugates, rotations, field reversal and exchange transformations. Multi-place nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry reductions. On the other hand, to solve multi-place nonlocal systems, one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group, such that the separated systems are coupled local ones. By using the separation method, all the known powerful methods used in local systems can be applied to nonlocal cases. In this review article, we take two-place and four-place nonlocal nonlinear Schrödinger (NLS) systems and Kadomtsev-Petviashvili (KP) equations as simple examples to explain how to derive and solve them. Some types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.     

光谱重置法在非局域空间光孤子研究中的应用

利用光谱重置法在数值上求解非局域非线性薛定谔方程,快速准确地计算出非局域非线性介质中空间光孤子的波形,并得到在不同非局域程度下形成孤子的临界功率和临界束宽的关系.研究结果表明,在任意非局域程度条件下都可以形成稳定的空间光孤子.在响应函数不同时分别与解析解进行对比,发现数值解和解析解只有在强非局域和弱非局域这两种极限条件下是一致的,并给出了对应解析解的有效范围.