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Quantum Nonlocality

Edited by Tomasz Bigaj (Warsaw University, University of Illinois at Springfield)
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Summary

The problem of quantum nonlocality emerged for the first time in the famous Einstein-Podolsky-Rosen argument against the orthodox (Copenhagen) interpretation of quantum mechanics. The EPR argument employs an entangled state of two particles in which the position and momentum of one particle are correlated respectively with the position and momentum of the other particle regardless of their spatial separation. Under the assumption that quantum mechanics is complete it follows that a measurement of a selected quantity on one particle instantaneously (superluminally) changes the state of the other particle, and this constitutes a standard example of nonlocal quantum correlations. The notion of quantum nonlocality plays an important role in Bell’s theorem, where the joint assumption of locality and realism of properties is shown to have a consequence violating quantum-mechanical predictions. It is common to distinguish two types of quantum nonlocality: outcome dependence and parameter dependence. Only the former is believed to be necessary to account for the predictions of standard quantum mechanics. Modern discussions of quantum nonlocality often rely on the general framework of modal logic, and in particular the logic of counterfactual conditionals.

Key works

The EPR argument in its standard version is laid out in the classic article Einstein et al 1935 . Bell’s theorem and its philosophical consequences are discussed in the seminal papers on the foundation of quantum mechanics collected in Bell 2004. The distinction between the two main types of quantum nonlocality is made in Jarrett 1984.

Introductions  Maudlin 2002, Berkovitz 2008
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  1. Samson Abramsky (2013). Relational Hidden Variables and Non-Locality. Studia Logica 101 (2):411-452.
    We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.
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  2. Guillaume Adenier, A. I͡U Khrennikov & Theo M. Nieuwenhuizen (eds.) (2006). Quantum Theory: Reconsideration of Foundations-3: Växjö, Sweden, 6-11 June 2005. American Institute of Physics.
    This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.
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  3. Diederik Aerts (2013). La mecánica cuántica y la conceptualidad: materia, historias, semántica y espacio-tiempo. Scientiae Studia 11 (1):75-99.
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  4. Diederik Aerts, Sven Aerts, Jan Broekaert & Liane Gabora (2000). The Violation of Bell Inequalities in the Macroworld. Foundations of Physics 30 (9):1387-1414.
    We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...)
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  5. Diederik Aerts, Jan Broekaert & Sonja Smets (1998). Inconsistencies in Constituent Theories of World Views: Quantum Mechanical Examples. [REVIEW] Foundations of Science 3 (2):313-340.
    We put forward the hypothesis that there exist three basic attitudes towards inconsistencies within world views: (1) The inconsistency is tolerated temporarily and is viewed as an expression of a temporary lack of knowledge due to an incomplete or wrong theory. The resolution of the inconsistency is believed to be inherent to the improvement of the theory. This improvement ultimately resolves the contradiction and therefore we call this attitude the ‘regularising’ attitude; (2) The inconsistency is tolerated and both contradicting elements (...)
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  6. Dirk Aerts (1982). Description of Many Separated Physical Entities Without the Paradoxes Encountered in Quantum Mechanics. Foundations of Physics 12 (12):1131-1170.
    We show that it is impossible in quantum mechanics to describe two separated physical systems. This is due to the mathematical structure of quantum mechanics. It is possible to give a description of two separated systems in a theory which is a generalization of quantum mechanics and of classical mechanics, in the sense that this theory contains both theories as special cases. We identify the axioms of quantum mechanics that make it impossible to describe separated systems. One of these axioms (...)
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  7. B. E. Allman, A. Cimmino, S. L. Griffin & A. G. Klein (1999). Quantum Phase Shift Caused by Spatial Confinement. Foundations of Physics 29 (3):325-332.
    This paper presents the results of optical interferometry experiments in which the phase of photons in one arm of a Mach-Zehnder interferometer is modified by applying a transverse constriction. An equivalent quantum interferometry experiment using neutron de Broglie waves is discussed in which the observed phase shift is in the spirit of the force-free phase shift of the Aharonov-Bohm effects. In the optical experiments the experimental results are in excellent agreement with predictions.
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  8. Renato M. Angelo (2009). On the Interpretative Essence of the Term “Interaction-Free Measurement”: The Role of Entanglement. [REVIEW] Foundations of Physics 39 (2):109-119.
    The polemical term “interaction-free measurement” (IFM) is analyzed in its interpretative nature. Two seminal works proposing the term are revisited and their underlying interpretations are assessed. The role played by nonlocal quantum correlations (entanglement) is formally discussed and some controversial conceptions in the original treatments are identified. As a result the term IFM is shown to be consistent neither with the standard interpretation of quantum mechanics nor with the lessons provided by the EPR debate.
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  9. Kevin Ann & Gregg Jaeger (2009). Finite-Time Destruction of Entanglement and Non-Locality by Environmental Influences. Foundations of Physics 39 (7):790-828.
    Entanglement and non-locality are non-classical global characteristics of quantum states important to the foundations of quantum mechanics. Recent investigations have shown that environmental noise, even when it is entirely local in influence, can destroy both of these properties in finite time despite giving rise to full quantum state decoherence only in the infinite time limit. These investigations, which have been carried out in a range of theoretical and experimental situations, are reviewed here.
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  10. I. Antoniou, E. Karpov & G. Pronko (2001). Non-Locality in Electrodynamics. Foundations of Physics 31 (11):1641-1655.
    We investigate the applicability of Hegerfeldts arguments on Quantum nonlocality in Quantum Electrodynamics following the work of Prigogine, Pronko, Petrosky, Ordonez and Karpov. We demonstrate the appearance of nonlocal effects at the level of quantum states. We show, however that the expectation values of some observables spread causally. Therefore the measurement of the nonlocality is questionable. We investigate an approach to classical measurement and conclude that the classical measurement cannot detect the “acausal” effects of the non-locality.
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  11. Frank Arntzenius (1994). Relativistic Hidden Variable Theories? Erkenntnis 41 (2):207 - 231.
    I show that for any quantum dynamics and any choice of observables as hidden variables an adequate hidden variable theory always exists. I argue that hidden variable theories have no more problems in reconciling non-locality with relativity than no-hidden-variable theories.
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  12. J. C. Aron (1981). Stochastic Foundation for Microphysics. A Critical Analysis. Foundations of Physics 11 (9-10):699-720.
    The stochastic scheme proposed in a previous paper as subjacent to quantum mechanics is analyzed in the light of the difficulties and criticisms encountered by similar attempts. It is shown that the limitation of the domain where the theory is valid gives a reply to the criticisms, but restricts its practical usefulness to the description of basic features. A stochastic approach of the hadron mass spectrum, allowing the scheme to emerge in the domain of experimental verification (to be worked out (...)
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  13. Richard T. W. Arthur (1981). Book Review:Quantum Mechanics, a Half Century Later J.L. Lopes, M. Paty. [REVIEW] Philosophy of Science 48 (1):156-.
  14. Alain Aspect & Robin Kaiser (1990). Linear Momentum Conservation in Coherent Population Trapping: A Case Study for a Quantum Filtering Process. [REVIEW] Foundations of Physics 20 (12):1413-1428.
    We discuss the question of linear momentum conservation when an atom coupled to a laser field enters into a state which is not an eigenstate of the linear momentum. Such a situation happens in the recently demonstrated laser cooling of atoms by velocity selective coherent population trapping. We show that this process can be understood as a filtering of the atomic state by the laser field taken as a classical measuring apparatus. In a different approach, the laser field can be (...)
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  15. D. Atkinson (1998). The Light of Quantum Mechanics. Dialectica 52 (2):103–126.
    It is argued that while classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering rst the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebu of the Copenhagen interpretation is shown to (...)
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  16. David Atkinson, Quantum Mechanics and Retrocausality.
    The classical electrodynamics of point charges can be made finite by the introduction of effects that temporally precede their causes. The idea of retrocausality is also inherent in the Feynman propagators of quantum electrodynamics. The notion allows a new understanding of the violation of the Bell inequalities, and of the world view revealed by quantum mechanics. Published in The Universe, Visions and Perspectives, edited by N. Dadhich and A. Kembhavi, Kluwer Academic Publishers, 2000, pages 35-50.
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  17. Harald Atmanspacher (2002). Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond. [REVIEW] Foundations of Physics 32 (3):379-406.
    The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.
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  18. Michael N. Audi (1973). Book Review:Perspectives in Quantum Theory: Essays in Honor of Alfred Lande Wolfgang Yourgrau, Alwyn Van Der Merwe. [REVIEW] Philosophy of Science 40 (2):323-.
  19. Jürgen Audretsch & Vladimir D. Skarzhinsky (1998). Quantum Processes Beyond the Aharonov-Bohm Effect. Foundations of Physics 28 (5):777-788.
    We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the (...)
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  20. Guido Bacciagaluppi (2013). Insolubility Theorems and EPR Argument. European Journal for Philosophy of Science 3 (1):87-100.
    I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility (...)
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  21. J. E. Baggott (2011). The Quantum Story: A History in 40 Moments. Oxford University Press.
    Prologue: Stormclouds : London, April 1900 -- Quantum of action: The most strenuous work of my life : Berlin, December 1900 ; Annus Mirabilis : Bern, March 1905 ; A little bit of reality : Manchester, April 1913 ; la Comédie Française : Paris, September 1923 ; A strangely beautiful interior : Helgoland, June 1925 ; The self-rotating electron : Leiden, November 1925 ; A late erotic outburst : Swiss Alps, Christmas 1925 -- Quantum interpretation: Ghost field : Oxford, August (...)
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  22. J. E. Baggott (2004). Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory. Oxford University Press.
    Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon and (...)
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  23. A. Baltag & S. Smets (2008). A Dynamic-Logical Perspective on Quantum Behavior. Studia Logica 89 (2):187 - 211.
    In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various (...)
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  24. Alexandru Baltag & Sonja Smets, The Logic of Quantum Programs.
    We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems. We give a syntax and a relational semantics in which we abstract away from phases and probabilities. We present a sound proof system for this logic, and we show how to characterize by logical means various forms of entanglement (e.g. the Bell states) and various (...)
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  25. Gergely Bana & Thomas Durt (1997). Proof of Kolmogorovian Censorship. Foundations of Physics 27 (10):1355-1373.
  26. Karen Michelle Barad (2007). Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning. Duke University Press.
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  27. F. Barone, A. O. Barut, E. Beltrametti, S. Bergia, R. A. Bertlmann, H. R. Brown, G. C. Ghirardi, D. M. Greenberger, D. Home & M. Jammer (1991). Bell's Theorem and the Foundations of Modern Physics. Foundations of Physics 21 (8).
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  28. Jeffrey A. Barrett (2001). The Strange World of Quantum Mechanics Daniel F. Styer. [REVIEW] British Journal for the Philosophy of Science 52 (2):393-396.
  29. Jeffrey A. Barrett (1999). Book Review: Quantum Chance and Non-Locality, by Michael Dickson. [REVIEW] Foundations of Physics 29 (6):1011-1018.
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  30. Jeffrey A. Barrett (2005). Relativistic Quantum Mechanics Through Frame-Dependent Constructions. Philosophy of Science 72 (5):802-813.
    This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions of spacetime maps and frame-dependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, they provide neither mechanical nor causal explanations for local quantum events. Rather, the hiddenvariable dynamics used in such constructions is just a rule that helps to characterize the set of all possible spacetime maps. But while having neither mechanical nor causal explanations of (...)
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  31. A. O. Barut (1992). How to Avoid “Quantum Paradoxes”. Foundations of Physics 22 (1):137-142.
    The “theorems” showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.
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  32. A. O. Barut, M. Božić & Z. Marić (1988). Joint Probabilities of Noncommuting Operators and Incompleteness of Quantum Mechanics. Foundations of Physics 18 (10):999-1012.
    We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond (...)
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  33. Angelo Bassi (ed.) (2006). Quantum Mechanics: Are There Quantum Jumps? Trieste, Italy, 5 Spetember -2005 and on the Present Status of Quantum Mechanics Lošinj, Croatia 7-9 September 2005. [REVIEW] American Institute of Physics.
    This conference brought together experts in different fields related to the foundations of quantum mechanics, ranging from mathematical physics to experimental physics, as well as the philosophy of science. The major topics discussed are: collapse models, Bohemian mechanics and their relativistic extensions, other alternative formulation of quantum mechanics, properties of entanglement, statistical physics and probability theory, new experimental results, as well as philosophical and epistemological issues.
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  34. H. Bechmann-Pasquinucci (2005). From Quantum State Targeting to Bell Inequalities. Foundations of Physics 35 (11):1787-1804.
    Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally entangled states. The optimal solution of the game is used to derive a Bell inequality for two entangled qutrits. We argue that the nice properties of the inequality are direct consequences of the method of construction.
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  35. Donald Bedford & Henry P. Stapp (1989). Nonlocal Character of the Rastall Model. Foundations of Physics 19 (4):397-406.
    The discussion of whether quantum theory is compatible with the locality idea that no causal influence can act outside the forward light cone has recently been tightly linked to the corresponding question for a much simpler model theory that enjoys all of the pertinent properties of quantum theory but is much easier to fully comprehend. It is shown here that, contrary to recent claims, the model theory is incompatible with the locality idea mentioned above. The logical structure of the argument, (...)
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  36. J. S. Bell (2004 [1964]). On the Einstein-Podolsky-Rosen Paradox. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 14--21.
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  37. J. S. Bell (2004). Atomic-Cascade Photons and Quantum-Mechanical Nonlocality. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 105--110.
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  38. J. S. Bell (2004). Bertlmann's Socks and the Nature of Reality. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 139--158.
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  39. J. S. Bell (2004). La Nouvelle Cuisine. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 232--248.
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  40. J. S. Bell (2004). On the Problem of Hidden Variables in Quantum Mechanics. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. 1--13.
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  41. J. S. Bell (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press.
    This book comprises all of John Bell's published and unpublished papers in the field of quantum mechanics, including two papers that appeared after the first edition was published. It also contains a preface written for the first edition, and an introduction by Alain Aspect that puts into context Bell's great contribution to the quantum philosophy debate. One of the leading expositors and interpreters of modern quantum theory, John Bell played a major role in the development of our current understanding of (...)
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  42. Js Bell (1992). 6 Possible Worlds of Quantum-Mechanics (Reprinted From Possible Worlds in Humanities Arts and Sciences, Pg 359-373, 1989. [REVIEW] Foundations of Physics 22 (10):1201-1215.
  43. Gordon Belot (1998). Understanding Electromagnetism. British Journal for the Philosophy of Science 49 (4):531-555.
    It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.
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  44. Darrin W. Belousek (2003). Non‐Seperability, Non‐Supervenience, and Quantum Ontology. Philosophy of Science 70 (4):791-811.
    An argument to the effect that quantum mechanics commits us to the existence of non-supervenient relations, and therefore that we should admit such relations into our quantum ontology as fundamental entities, has been given by Teller and reformulated by French. This paper aims, first, to explicate and evaluate that argument; second, to extend its premises in order to assess its relevance for other interpretations of quantum mechanics; and, third, to clarify its implications for holism and individuation in quantum ontology.
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  45. Darrin W. Belousek (1997). Perspectives on Quantum Reality: A Critical Survey. Studies in History and Philosophy of Science Part B 28 (3):415-420.
  46. Y. Ben-Aryeh, A. Mann & B. C. Sanders (1999). Empirical State Determination of Entangled Two-Level Systems and Its Relation to Information Theory. Foundations of Physics 29 (12):1963-1975.
    Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger than that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt and Hilbert-Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does (...)
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  47. Y. Ben-Menahem (2002). Quantum Theory and the Flight From Realism - Christopher Norris, Routledge, London, New York, IX +266pp., $26.00 Paperback, ISBN 0-415-22322-. [REVIEW] Studies in History and Philosophy of Science Part B 33 (3):587-591.
  48. Yemima Ben-Menahem (1997). Dummett Vs Bell on Quantum Mechanics. Studies in History and Philosophy of Science Part B 28 (2):277-290.
  49. S. Bergia & F. Cannata (1982). Higher-Order Tensors and Tests of Quantum Mechanics. Foundations of Physics 12 (9):843-859.
    We illustrate a generalization of Bell's inequality which is not limited to spin-1/2 or photon systems and does not depend on model-dependent assumptions. We then construct a specific class of examples, in terms of the decaying state and the correlated observables to be measured on the decay products, for which this inequality is violated by quantum mechanics. Finally we discuss the basic and practical problems involved in the measurement of these correlations.
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  50. János A. Bergou (1999). Entangled Fields in Multiple Cavities as a Testing Ground for Quantum Mechanics. Foundations of Physics 29 (4):503-519.
    Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...)
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