International Journal of Quantum Information

ENTANGLEMENT, LOCALITY, AND SEPARABILITY: A TREATISE ON DIFFERENT VIEWPOINTS

THOMAS KESSEMEIER, Thomas Krüger

Published Feb 1, 2007• 1 citation

Abstract

Within the framework of a statistical interpretation of quantum mechanics, entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell's inequality Δ ≤ 2. How can these different viewpoints be reconciled? We first show that (non-)separability follows different laws to (non-)locality, and, moreover, it is much more difficult to characterize as long as the mostly employed operational rather than an ontic definition of separability is used. In consequence, (i) "entanglement" has two different meanings which may or may not be realized simultaneously on one and the same ensemble, and (ii) we have to disadvise the use of the common separability definition which is still employed by the majority of the physical community.

DOI: 10.1142/s0219749907002839

Related papers

Entanglement: non-separability

Gennaro Auletta, Mauro Fortunato, Giorgio Parisi A

In classical mechanics, two (or more) systems that do not interact – that do not exert any kind of force on each other – are completely separated (see Sec. 1.1), i.e. experiments performed locally on one of them cannot in any way influence experiments performed locally on the other. Quantum mechanics, on the other hand, admits that there can be a form of interdependence even in absence of physical interaction. This type of correlation goes under the name of entanglement (see Def. 5.1: p. 183). We already know that entanglement means non-factorizability of the state vector describing a system with at least two different degrees of freedom. In this chapter, we shall see that this may be the case also for systems that are very far away (space-like distant) from each other and we shall learn many interesting consequences of this state of affairs. Recent developments show that one may entangle even particles that have never interacted with each other. The starting point of the following analysis is necessarily represented by the pioneering paper of Einstein, Podolsky, and Rosen, who inaugurated an incredible series of theoretical and experimental investigations right up to the present day that have confirmed the predictions of quantum mechanics. The “irony” of this history is that Einstein, Podolsky, and Rosen, EPR for short, aimed to present a definitive proof of the inconsistency of quantum mechanics relative to classical physical theory. In fact, they initiated one of the most prolific fields of modern science.

Cambridge University Press eBooksApr 16, 20090 citations

THOUGHTS ON NON-LOCALITY AND QUANTUM MECHANICS

William George Unruh

The debate about the non-locality of quantum mechanics is old, but still lively. Numerous people use non-locality as (bad) shorthand for quantum entanglement. But some have a long-standing commitment to the validity of this characterization. This paper examines two separate streams in this debate. The first is the arguments of Stapp, and especially his recent paper where he simplifies his contractual argument in the Hardy situation to argue for the non-locality of quantum mechanics. He has maintained his contention that an analysis of a Hardy-type correlation between two spatially separated observers proves that quantum mechanics itself is non-local, without any additional assumption of realism or hidden variables. In the second section, I try to carefully examine the Bell argument in the CHSH variant to see where the difference between the quantum and classical situations differ. Asher Peres was one of the great physicists of the late 20th century, especially for his intense concern with the fundamental nature of quantum mechanics. His courage in devoting his life to an area many considered "philosophical" (i.e. non-physical) paved the way for the rest of us to reveal our interests and confusions about this area. I am not sure that he would agree with everything in this paper, but I offer it as a tribute to him.

International Journal of Quantum InformationFeb 1, 20064 citations

Non-Locality and Quantum Theory: New Experimental Evidence

Luigi Accardi, Massimo Regoli

Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooksFeb 24, 200613 citations

Operational approach to the entanglement

Marian Kupczyński

In early days of quantum theory it was believed that the results of measurements performed on two distant physical systems should be uncorrelated thus their quantum state should be separable it means described by a simple tensor product of the individual local state vectors or a tensor product of individual local density operators. It was shown many years ago by EPR that two systems which interacted in the past and separated afterwards had to be described in most cases by particular non-separable states which are called entangled. It was noticed by Zanardi et al. that a Hilbert space of possible state vectors of compound physical system could be partitioned in different way by introducing various tensor product structures induced by the experimentally accessible observables (interactions and measurements). Therefore a separable state in one partition could become entangled in different partition. In this sense the entanglement was relative to a particular set of experimental capabilities. Continuing this line of thought Torre et al. claimed to prove that for any separable state there existed strongly correlated physical observables therefore all quantum states were entangled. The same claims one may find in several recent papers. In this paper we will discuss in operational way the differences existing between separable, non-separable and entangled states and we will show that the conclusions of Torre et al. were unjustified. A sufficient condition for entanglement is the violation of BI-CHSH and/or steering inequalities. Since there exist experiments outside the quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon.

arXiv:1208.6532Aug 31, 20120 citations

A Stronger Bell Argument for Quantum Non-Locality

Paul M. Näger

It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a stronger Bell argument which even forbids certain non-local theories. Among these excluded non-local theories are those whose only non-local connection is a probabilistic (or functional) dependence between the space-like separated measurement outcomes of EPR/B experiments (a subset of outcome dependent theories). In this way, the new argument shows that the result of the received Bell argument, which requires just any kind of non-locality, is inappropriately weak. Positively, the remaining non-local theories, which can violate Bell inequalities (among them quantum theory), are characterized by the fact that at least one of the measurement outcomes in some sense probabilistically depends both on its local as well as on its distant measurement setting (probabilistic Bell contextuality). Whether an additional dependence between the outcomes holds, is irrelevant for the question whether a certain theory can violate Bell inequalities. This new concept of quantum non-locality is considerably tighter and more informative than the one following from the usual Bell argument. We prove that (given usual background assumptions) the result of the stronger Bell argument presented here is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level.

Aug 15, 20137 citations

Experiment Data Indicates Quantum Entanglement May not be Non-Local

Krishan Vats

This is a statistical analysis of the experimental data used in a recent paper [M. Giustina et al, Phys. Rev. Lett. 115, 250401 (2015)], published at https://arxiv.org/abs/1511.03190. The data for this analysis was graciously made available by the authors as a private communication. This article is not meant in any way to comment upon the originally published findings of the experiment. Abstract – Till date, all experiments prove non-locality of quantum entanglement based upon overall statistical correlations and thus demonstrating that Bell’s inequality is violated. No detailed data analysis has been published yet. This article presents a first of its kind experimental analysis and it indicates that there is a real chance that entanglement may be local. This is a huge claim by any means. But it is necessary to make such dramatic claim due to two reasons – 1) It is based upon experimental data and can be tested and verified. 2) So that the QM community makes an effort to analyze detailed data to scrutinize the reality of entanglement. Due to large amount of data involved, experimentalists only look at data at aggregate level and do not scrutinize the raw data in full detail. When data of this experiment was analyzed at detail level, it was observed that non-locality of entanglement can not be settled until this kind of analysis is completed on data from multiple such experiments. The natural and prompt reaction from many may be to look for faults with this analysis without presenting the evidence that such analysis has already been completed. For curious people, observation is odd enough to be probed further. The complacent ones will look only for the faults, but those who welcome scrutiny, will challenge it with evidence and/or their own analysis at this detailed level. All sound theories welcome scrutiny and refute it with evidence. This article does not claim “classical mechanics” to be the solution. Quantum Mechanics predictions are correct in terms of averages. This analysis indicates that the statistical correlation percent of entanglement may be guided/balanced by some real/local mechanism rather than being independently probabilistic and spooky. It presents an intuitive mechanism that can explain statistical correlations without entanglement being non-local or entanglement being defined in a different way then it currently is. The scope of this article is only statistical data. Anti correlation (Bell’s state, when measured in the same angle) is always true, therefore it is not statistical in nature and is left out of scope. Moreover perfect anti correlation can easily be explained as a direct consequence of conservation laws. In fact, perfect anti correlation is a big red flag to the probabilistic nature. There is no such thing as zero, or one probability. Zero or one probability would actually be a law, not probability. So, perfect anti correlation itself indicates that the outcomes of entanglement can not be probabilistic; they have to be governed by law, not probability. If some balancing mechanism is found to exist then (in terms of magnitude), it really operates within probabilistic limits thereby making it very difficult to differentiate it from probabilistic nature. Therefore a detailed data analysis on many such experiments is necessary to rule it in/out. In fact it would require special experiments for its independent investigation. This can also explain why the correlations have been considered probabilistic for such a long history. Therefore, this type of experimental investigation is a must in order to conclude existence/nonexistence of non-local entanglement. By the time this revision is written, another experiment has been analyzed and published at http://vixra.org/abs/1611.0148 Both of the recent experiments give similar indications.

Sep 1, 20160 citations