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arXiv:quant-ph/0503007

How come the Correlations?

Nicolas Gisin

Published Mar 1, 2005• 5 citations
arXivHTMLPDF

Abstract

In relativity there is space-time out there. In quantum mechanics there is entanglement. Entanglement manifests itself by producing correlations between classical events (e.g. the firing of some detectors) at any two space-time locations. If the locations are time-like separated, i.e. one is in the future of the other, then there is no specific difficulty to understand the correlations. But if the two locations are space-like separated, the problem is different. How can the two space-time locations out there know about what happens in each other without any sort of communication? If space-time really exists, the locations must do something like communicating. Or it was all set up at the Beginning. But the correlations depend also on the free choice of the experimentalists, one in each space-time location. This allowed John Bell to derive his inequality and the experimentalists to violate it, thus refuting the assumption that it was all set up at the beginning: the Correlations can't be explained by common causes.

DOI
10.48550/arxiv.quant-ph/0503007

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In relativity there is space-time out there. In quantum mechanics there is entanglement. Entanglement manifests itself by producing correlations between classical events (e.g. the firing of some detectors) at any two space-time locations. If the locations are time-like separated, i.e. one is in the future of the other, then there is no specific difficulty to understand the correlations. But if the two locations are space-like separated, the problem is different. How can the two space-time locations out there know about what happens in each other without any sort of communication? If space-time really exists, the locations must do something like communicating. Or it was all set up at the Beginning. But the correlations depend also on the free choice of the experimentalists, one in each space-time location. This allowed John Bell to derive his inequality and the experimentalists to violate it, thus refuting the assumption that it was all set up at the beginning: the Correlations can't be explained by common causes.
In recent decades it was established that the measurements of physical quantities in space-time points divided by large space-like intervals can be correlated.The correlation is created by the measurements while their mutual influence requires the corresponding supraliminal velocities.This situation is commonly known as the violation of the Bell inequality in the Bohm version of Einstein-Podolsky-Rosen paradox.Nearly 40 years the question remains disputable with a variety of contradicting views.The most frequently the violation is explained by the existence of some momentary action at a distance which obliges the quantum mechanics (as well as all nature) to be nonlocal.We find the "common cause in the past" as the origin of the observed quantum correlation which so far was unnoticed either by the partisans of quantum non-locality or their opponents.The novelty of our approach is the accent on the expressions for the observed physical quantities rather than on the "entangled" two-particle wave functions.We show the crucial role of phases in the correlation process that is hard to notice using the traditional approach.
The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. We show that the processes realizable by classically controlled quantum circuits are ECS and conjecture that the reverse also holds.
Standard common causal explanations of the EPR situation assume a so-called joint common cause system that is a common cause for all correlations. However, the assumption of a joint common cause system together with some other physically motivated assumptions concerning locality and no-conspiracy results in various Bell inequalities. Since Bell inequalities are violated for appropriate measurement settings, a local, non-conspiratorial joint common causal explanation of the EPR situation is ruled out. But why do we assume that a common causal explanation of a set of correlation consists in finding a joint common cause system for all correlations and not just in finding separate common cause systems for the different correlations? What are the \nperspectives of a local, non-conspiratorial separate common causal explanation for the EPR scenario? And finally, how do Bell inequalities relate to the weaker assumption of separate common cause systems? \n
The Classic Physics and the Quantum Physics are two branches of the nowadays Science of Physics, which are still incompatible. Einstein's Relativity theories, which are the leading acceptable theories of the nowadays Classic Physics, present the Universe as a "Block Universe", in which Time is not a flow of events, where the past vanishes and does not exist anymore, and the future is not yet created. Instead, the "Block Universe" model presents that the past, present and future are all equally real and coexist tenselessly, and everything, the past, present and future are all predefined and engraved in that "Block Universe" model of the Universe. On the other hand, the Quantum Mechanics presents, that the future is created continuously when particles interact with the environment, and the state of each particle is presented by what the Quantum Mechanics denotes as the "Wave Function" which presents the probabilities to find the particle in various locations, such that, before the particle is measured, or interacts with the environment, it can actually be in all those locations at once, and only after the particle is measured, or interacts with the environment, the "Wave Function Collapses" and the particle "chooses" randomly, to be only in one specific location. Actually, that "Wave Function Collapse" is one of the most mysterious phenomena in Physics. But it seems that Bell's Theorem, and the experiments that followed it, settled that long debate about it, providing the means to establish that the Quantum Mechanics view on this matter is the correct view and the Classic Physics and Einstein's Relativity theories view on this matter is not correct. Bell's Inequality provided the logic and the mathematics behind this decision, and physicists such as Alain Aspect, John Clauser and Anton Zeilinger, who also won the Nobel prize on that, provided the experimental justification. However, although the above debate was settled, there is also still a need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. The author of this paper refers to additional papers, by the author of this paper, which present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time. These additional papers propose to replace the Einstein's "Block Universe" model of the Universe with an alternate model, of a Multi-Space-Times model of the Universe, in which, each Energy might embed its own private Space-Time facet, or attribute, such that each such Space-Time cannot be considered to be a real entity, that really exists in the Universe. And this paper argues, that Bell's Theorem, and the experiments that followed it, might be also used to support the above-mentioned Multi-Space-Times model of the Universe, and this might also fill in the above-mentioned gap, which might be the need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. In addition to the above, the above-mentioned additional papers, also propose additional experiments, based only on the Classic Physics, which if implemented successfully, might provide additional validity to the proposed Multi-Space-Times model of the Universe. The support that might be provided to the proposed model, of a Multi-Space-Times of the Universe, by the Bell's Theorem, and the experiments that followed it, is still based on the Quantum Mechanics. Thus, because these additional experiments, proposed in the above-mentioned additional papers, are based only on the Classic Physics, this might also provide a lead for further narrowing the gap between the Classic Physics and the Quantum Physics. Thus, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the proposed Multi-Space-Times model of the Universe, as presented in the above-mentioned papers, should be an important and a significant endeavor.
In recent decades it was established that the quantum measurements of physical quantities in space-time points divided by space-like intervals may be correlated. Though such correlation follows from the formulas of quantum mechanics its physics so far remains unclear and there is a number of different and rather contradictory interpretations. They concern particularly the so-called Einstein-Podolsky-Rosen paradox where the momentary action at a distance together with non-local entangled states is used for the interpretation. We assume that the quantum theory can be formulated as local and look for the consequences of this assumption. Accordingly we try to explain the correlation phenomena in a local way looking for the origin of correlation. To exclude a presupposed correlation of participating quantum particles we consider two independent particle sources and two detectors that are independent as well. We show that the origin of the correlation is the feature that the occupation number of a particle (and other its measurable quantities) is formed by a pair of complex conjugated wave functions with in general arbitrary phases. We consider this point as crucial as it provides interpretation of the observed correlation phenomena that may otherwise look puzzling. We briefly discuss a special type of noise that is typical for the quantum correlation phenomena.
In his seminal paper, Bell [Physics Physique Fizika 1, 195 (1964)] considers the correlations that result from space-like separated measurements on a pair of entangled particles. He uses relativity theory to motivate the Bell causal structure, then shows the existence of quantum correlations that cannot be explained classically within this causal structure. Classical explanations of such quantum correlations are possible in alternative causal structures, for instance, those that allow superluminal causal influences, but, as shown in [New Journal of Physics 17 033002 (2015)], all such alternative explanations require fine tuning (causation without correlation). Here we discuss the existence of spurious quantum correlations --- correlations that look quantum in one causal structure, but have a natural classical explanation in another. More precisely, there are causal structures that admit non-classical quantum correlations, but for which the same correlations have a classical explanation in another causal structure without fine tuning. The realisation in the other causal structure can also be achieved without breaking any natural constraints on the causal structure that follow from relativity theory. However, similarly to non-classical quantum correlations in the Bell causal structure, we find other causal structures with non-classical quantum correlations that do not have a classical causal explanation in any alternative causal structure without fine tuning.