It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is (...) no reason to suspect any conflict between quantum theory and special relativity. (shrink)

We show that local realism applied to states characterized by a single quantum equally and coherently shared between a number of qubits (so-called W states) produces predictions incompatible with quantum theory. The origin of this incompatibility is shown to originate from the destructive interference of amplitude probabilities associated with nonlocal states, a phenomenon that has no classical analog.

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or (...) that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research. (shrink)

“Elements of reality” are defined as in the work of Einstein, Podolsky, and Rosen. It is further assumed that the sum or product of twocommuting elements of reality also is an element of reality. An algebra contradiction ensues.

A quantum algorithm succeeds not because the superposition principle allows ‘the computation of all values of a function at once’ via ‘quantum parallelism’, but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information‐processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I (...) also introduce the notion of ‘pseudotelepathic’ games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players’ correlated responses in a game). *Received October 2008. †To contact the author, please write to: Department of Philosophy, University of Maryland, College Park, MD 20742; e‐mail: [email protected]. (shrink)

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account of the nature of quantum information. (...) Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These (...) include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics for it. We conclude with a philosophical discussion on the interpretation of quantum mechanics. (shrink)

This essay is a discussion of the philosophical and foundational issues that arise in non-relativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and non-locality. In each case, the main point is to give the reader some introductory understanding of some of the major issues and recent ideas.

We discuss a recent work by J. Lawrence et al. [arxiv.org/abs/2208.11793] criticizing relational quantum mechanics (RQM) and based on a famous nonlocality theorem Going back to Greenberger Horne and Zeilinger (GHZ). Here, we show that the claims presented in this recent work are unjustified and we debunk the analysis.

The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...) particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together. (shrink)

There are hints that the connectivity of space-time in quantum gravity could emerge from entanglement, and it has further been proposed that any two entangled particles may be connected by a quantum wormhole. One way to test this proposal is by probing the electric field of an entangled charged particle to determine whether its electric field leaks through the putative wormhole. In addition, if such a wormhole is traversable, then it could be possible for the collapse of the wave function (...) to occur in a causal manner, with information about the collapse travelling through the wormhole at the speed of light, rather than the wave function collapse being a global and instantaneous event. (shrink)

This is an extended essay review of Tanya and Jeffrey Bub’s Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors’ artistic choices in the context of comics theory. Although Totally Random does not defend any particular interpretation of quantum mechanics, we find that, in its mode of presentation, Totally Random is a (...) beautiful expression and illustration of the information-theoretic interpretation and its value. (shrink)

In this paper we address a deeply interesting debate that took place at the end of the last millennia between David Mermin, Adan Cabello and Michiel Seevinck, regarding the meaning of relationalism within quantum theory. In a series of papers, Mermin proposed an interpretation in which quantum correlations were considered as elements of physical reality. Unfortunately, the very young relational proposal by Mermin was too soon tackled by specially suited no-go theorems designed by Cabello and Seevinck. In this work we (...) attempt to reconsider Mermin's program from the viewpoint of the Logos Categorical Approach to QM. Following Mermin's original proposal, we will provide a redefinition of quantum relation which not only can be understood as a preexistent element of physical reality but is also capable to escape Cabello’s and Seevinck's no-go-theorems. In order to show explicitly that our notion of ontological quantum relation is safe from no-go theorems we will derive a non-contextuality theorem. We end the paper with a discussion regarding the physical meaning of quantum relationalism. (shrink)

According to the Gottesman–Knill theorem, quantum algorithms that utilize only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this article that this conclusion is misleading. First, the statement of the theorem is, on reflection, already evident when we consider Bell’s and related inequalities in the context of (...) a discussion of computational machines. This, in turn, helps us to understand that the appropriate conclusion to draw from the Gottesman–Knill theorem is not that entanglement is insufficient to enable a quantum performance advantage, but rather that if we limit ourselves to the operations referred to in the Gottesman–Knill theorem, we will not have used the resources provided by an entangled quantum system to their full potential. (shrink)

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the (...) uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics. (shrink)

I argue that our judgements regarding the locally causal models that are compatible with a given constraint implicitly depend, in part, on the context of inquiry. It follows from this that certain quantum no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of the possible implications (...) of this for our understanding of the limits of classical description, and for our understanding of the fundamental aim of physical investigation. _1_ Introduction _2_ No-Go Results _2.1_ The CHSH inequality _2.2_ The GHZ equality _3_ Classically Simulating Quantum Statistics _3.1_ GHZ statistics _3.2_ Singlet statistics _4_ What Is a Classical Computer Simulation? _5_ Comparing the All-or-Nothing GHZ with Statistical equalities _6_ General Discussion _7_ Conclusion. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In some cases, the effect of transmitting quantum bits cannot be (...) achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement. (shrink)

Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin-1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; (...) through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables are found, all the problems of quantum field theory and of quantum gravity might melt away. (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Within such analyses, it has been argued that locality is equivalent to determinism, given the strict correlations of quantum mechanics. However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. The latter analysis is carried out, and it is shown that, given certain definitions of locality and determinism for completely dynamical models, locality (...) implies, but is not implied by, determinism. Further, it is suggested that a local deterministic model has not been ruled out by Bell's theorem. It is suggested that such a model could naturally deny the independence of initial complete states from the settings of the apparatuses (a crucial assumption in the derivation of Bell's inequality). (shrink)

It is argued that probability should be defined implicitly by the distributions of possible measurement values characteristic of a theory. These distributions are tested by, but not defined in terms of, relative frequencies of occurrences of events of a specified kind. The adoption of an a priori probability in an empirical investigation constitutes part of the formulation of a theory. In particular, an assumption of equiprobability in a given situation is merely one hypothesis inter alia, which can be tested, like (...) any other assumption. Probability in relation to some theories – for example quantum mechanics – need not satisfy the Kolmogorov axioms. To illustrate how two theories about the same system can generate quite different probability concepts, and not just different probabilistic predictions, a team game for three players is described. If only classical methods are allowed, a 75% success rate at best can be achieved. Nevertheless, a quantum strategy exists that gives a 100% probability of winning. (shrink)

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection (...) includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony. Among the editors and contributors are John Clauser and Anton Zeilinger, recipients of the Nobel Prize in Physics 2022. (shrink)

This paper puts forward an ontology that is indebted to QBism, Kant, Bohr, Schrödinger, the philosophy of the Upanishads, and the evolutionary philosophy of Sri Aurobindo. Central to it is that reality is relative to consciousness or experience. Instead of a single mind-independent reality, there are different poises of consciousness, including a consciousness to which “we are all really only various aspects of the One”. This ontology helps clear up unresolved issues in the philosophy of science, such as arise from (...) the reification of quantum states or from disregard of the universal context of science, which is human experience. It further helps clear up unresolved issues in the philosophy of mind, in particular the problem of intentionality and the dilemma posed by the mutual inclusion of self and world. (shrink)

One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite (...) collection of probability zero events whose disjunction exhausts the space of experimental possibilities. (shrink)

Sir K. R. Popper's experimental schemes challenge the Copenhagen interpretation of quantum theory, principally Heisenberg's indeterminacy relations and the EPR paradox. “The so-called Einstein-Podolsky-Rosen paradox is not a paradox. It is a theoretical statement in expectation of an interpretation,” says K. R. Popper in this interview. “My experiment ought to be a classical experiment. It is very simple and free from any additional assumption. It should really be done.”.

We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of nonlocality. (...) 1 Introduction 2 Albert and Loewer's interpretation 3 Probabilities in Lockwood's interpretation 4 Sets of minds and their correlations 5 Many minds and GHZ. (shrink)

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. and Bell emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the (...) experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...) spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

This article considers the relationships between the character of physical law in quantum theory and Bohr’s concept of complementarity, under the assumption of the unrepresentable and possibly inconceivable nature of quantum objects and processes, an assumption that may be seen as the most radical departure from realism currently available. Complementarity, the article argues, is a reflection of the fact that, as against classical physics or relativity, the behavior of quantum objects of the same type, say, all electrons, is not governed (...) by the same physical law in all contexts, specifically in complementary contexts. On the other hand, the mathematical formalism of quantum mechanics offers correct probabilistic or statistical predictions in all contexts, here, again, under the assumption that quantum objects themselves and their behavior are beyond representation or even conception. Bohr, in this connection, spoke of “an entirely new situation as regards the description of physical phenomena that, the notion of complementarity aims at characterizing.” The article also considers the relationships among complementarity, entanglement, and quantum information, by basing these relationships on this understanding of complementarity. (shrink)

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a (...) single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated. (shrink)

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, (...) liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive “logic”). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems. (shrink)

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument be modified (...) in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell. (shrink)

The main formal structures of generalized quantum theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.

** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. ** A large part of this dissertation is devoted to understanding different aspects of four different kinds of correlations: local, partially-local, no-signaling and quantum mechanical correlations. Novel characteristics of these correlations have been used to study how they are related and how they can be (...) discerned via Bell-type inequalities that give non-trivial bounds on the strength of the correlations. ** The study of quantum correlations has also prompted us to study a) the multi-partite qubit state space with respect to its entanglement and separability characteristics, and b) the differing strength of the correlations in separable and entangled qubit states. Results include a novel classification of multipartite (partial) separability and entanglement, strong constraints on the monogamy of entanglement and of non-local correlations, and many new entanglement detection criteria that are directly experimentally accessible. ** Because of the generality of the investigation these results also have strong foundational as well as philosophical repercussions for the different sorts of physical theories as a whole; notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy. (shrink)

The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: (...) in the real-vector-space theory, there exist states of arbitrarily many binary objects, “rebits,” in which every rebit in the system is maximally entangled with each of the other rebits. (shrink)

The paper intends to provide an algebraic framework in which subluminal causation can be analysed. The framework merges Belnap's 'outcomes in branching time' with his 'branching space-time' (BST). it is shown that an important structure in BST, called 'family of outcomes of an event', is a boolean algebra. We define next non-stochastic common cause and analyse GHZ-Bell theorems. We prove that there is no common cause that accounts for results of GHZ-Bell experiment but construct common causes for two other quantum (...) mechanical setups. Finally, we investigate why some setups allow for common causes whereas other setups do not. (shrink)

After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.

The paper investigates, in the framework of branching space–times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.

Hardy’s non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is ‘possibilistic’ in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy’s paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurrence of Hardy’s paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy’s paradox is not true (...) more generally: we find a new ‘proof without inequalities’ in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality. (shrink)

An attempt is made to defend realism and the absence of space-like causation in quantum mechanics, by invoking indeterminism and a new necessary condition for stochastic causality, we term robustness. This condition is defended against recent critical attacks by Cartwright and Jones, and by Healey, and the violation of the robustness condition in Bell-type correlation experiments is shown to follow if an appropriate interpretation of the state vector is employed.

The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger (...) program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect. (shrink)

The Greenberger–Horne–Zeilinger argument against noncontextual local hidden variables is recast in quantum logical terms of fundamental propositions, states and probabilities. Unlike Kochen–Specker- and Hardy-like configurations, this operator based argument proceeds within four nonintertwining contexts. The nonclassical performance of the GHZ argument is due to the choice or filtering of observables with respect to a particular state. We study the varieties of GHZ games one could play in these four contexts, depending on the chosen state of the GHZ basis.

Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the (...) Clauser–Horne–Shimony–Holt inequality. (shrink)

When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum “population oscillations”, which can be seen as a generalized Hong-Ou-Mandel effect, (...) although they do not always correspond to even-odd oscillations. (shrink)