Alternative theories to quantum mechanics motivate important fundamental tests of our understanding and descriptions of the smallest physical systems. Here, using spontaneous parametric downconversion as a heralded single-photon source, we place experimental limits on a class of alternative theories, consisting of classical field theories which result in power-dependent normalized correlation functions. In addition, we compare our results with standard quantum mechanical interpretations of our spontaneous parametric downconversion source over an order of magnitude in intensity. Our data match the quantum mechanical (...) expectations, and do not show a statistically significant dependence on power, limiting quantum mechanics alternatives which require power-dependent autocorrelation functions. (shrink)

In this paper, I try to cause some good-natured trouble. The issue is, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained (...) application of the latest fad to a time-honoured problem, this method holds promise precisely because a large part---but not all---of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. (shrink)

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach (...) gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered. (shrink)

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution (...) based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules. (shrink)

Teilhard is among the first to seriously explore the future of human evolution. He advocates both bio-technologies (e.g. genetic engineering) and intelligence technologies. He discusses the emergence of a global computation - communication system (and is said by some to have been the first to have envisioned the Internet). He advocates the development of a global society. He is almost surely the first to discuss the acceleration of technological progress to a Singularity in which human intelligence will become super-intelligence. He (...) discusses the spread of human intelligence into the universe and its amplification into a cosmic-intelligence. His work has been taken up by Barrow and Tipler; Tipler; Moravec; and Kurzweil. Of course, Teilhard's Omega Point Theory is deeply Christian. For secular transhumanists, this may be difficult. But transhumanism cannot avoid a fateful engagement with Christianity. Christian institutions may support or oppose transhumanism. Since Christianity is an extremely powerful cultural force in the West, it is imperative for transhumanism to engage it carefully. A serious study of Teilhard can help that engagement and will thus be rewarding to both communities. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective (...) probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (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)

The famous EPR article of 1935 challenged the completeness of quantum mechanics and spurred decades of theoretical and experimental research into the foundations of quantum theory. A crowning achievement of this research is the demonstration that nature cannot in general consist in noncontextual pre-measurement properties that uniquely determine possible measurement outcomes, through experimental violations of Bell inequalities and Kochen-Specker theorems. In this article, I reconstruct an argument from Niels Bohr’s writings that the reality of the Einstein-Planck-de Broglie relations alone implies (...) that no such properties can exist for momentum and position measurements, show how this argument responds to the challenge of EPR on general physical grounds, and advance that this reconstruction shows that and how Bohr’s “complementarity” is a view of the objective content and logic of quantum theory. (shrink)

In quantum foundations, there is growing interest in the program of reconstructing the quantum formalism from clear physical principles. These reconstructions are formulated in an operational framework, deriving the formalism from information-theoretic principles. It has been recognized that this project is in tension with standard _ψ-ontic_ interpretations. This paper presupposes that the quantum reconstruction program (QRP) (i) is a worthwhile project and (ii) puts pressure on _ψ-ontic_ interpretations. Where does this leave us? Prima facie, it seems that _ψ-epistemic_ interpretations perfectly (...) fit the spirit of information-based reconstructions. However, _ψ-epistemic_ interpretations, understood as saying that the wave functions represents one’s _knowledge_ about a physical system, recently have been challenged on technical and conceptual grounds. More importantly, for some researchers working on reconstructions, the lesson of successful reconstructions is that the wave function does _not_ represent objective facts about the world. Since knowledge is a factive concept, this speaks against epistemic interpretations. In this paper, I discuss whether _ψ-doxastic_ interpretations constitute a reasonable alternative. My thesis is that if we want to engage QRP with _ψ-doxastic_ interpretations, then we should aim at a reconstruction that is spelled out in non-factive experiential terms. (shrink)

Recently there have emerged an assortment of theorems relating to the ‘absoluteness of emerged events,’ and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical non-absoluteness, such as relationalism or perspectivalism. However, in our view a close examination of these theorems fails to convincingly support such possibilities. In this paper we argue that the Wigner’s friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all (...) best understood as demonstrating that if quantum mechanics is universal, and if certain auxiliary assumptions hold, then the world inevitably includes various forms of ‘disaccord,’ but this need not be interpreted in a metaphysically radical way; meanwhile, the theorem of Ormrod and Barrett is best understood either as an argument for an interpretation allowing multiple outcomes per observer, such as the Everett approach, or as a proof that quantum mechanics cannot be universal in the sense relevant for this theorem. We also argue that these theorems taken together suggest interesting possibilities for a different kind of relational approach in which _interaction_ states are relativized whilst observed events are absolute, and we show that although something like ‘retrocausality’ might be needed to make such an approach work, this would be a very special kind of retrocausality which would evade a number of common objections against retrocausality. We conclude that the non-absoluteness theorems may have a significant role to play in helping converge towards an acceptable solution to the measurement problem. (shrink)

Classical systems of mereology identify a maximuml set of jointly exhaustive and pairwise disjoint (RCC5) relations. The amount of information that is carried by each member of this set of (crisp) relations is determined by the number of bits of information that are required to distinguish all the members of the set. It is postulated in this paper, that vague mereological relations are limited in the amount of information they can carry. That is, if a crisp mereological relation can carry (...) N bits of information, then a vague mereological relation can carry only 1 ⩽ n < N bits. The aim of this paper is it to explore these ideas in the context of various systems of vague mereological relations. The resulting formalism is non-classical in the sense of quantum information theory. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall (...) see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens : 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable. (shrink)

Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.

At the end of the 19th century, Josiah Royce participated in what has come to be called the great debate (Royce, 1897; Armour, 2005).1 The great debate concerned issues in metaphysical theology, and, since metaphysics was primarily idealistic, it dealt considerably with the relations between the divine Self and lesser selves. After the great debate, Royce developed his idealism in his Gifford Lectures (1898-1900). These were published as The World and the Individual. At the end of the first volume, Royce (...) added a Supplementary Essay. The Essay, continuing themes from the great debate, developed an intriguing mathematical model of the relations between the divine Self and lesser selves. The second volume went on to.. (shrink)

Recently I posted a paper entitled “External observer reflections on QBism”. As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism’s creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism’s features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism (...) might be interesting and useful for other experts in quantum foundations and quantum information theory. In the present paper I correct some of my earlier posted critical comments on QBism. At the same time, other critical comments gained new validation through my recent deeper understanding of QBists views on a number of problems. (shrink)

Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information (...) are no longer rival, but different interpretations of a single formal concept. (shrink)

In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s theory is confined to coding theorems. The attempt to extend the analogy beyond this original scope leads to a concept of quantum information that becomes indistinguishable from that (...) of quantum state. But information is essentially linked with communication, as it is clear in both Shannon’s and Schumacher’s proposals. If we detach information from this link, we are not talking about information but about quantum mechanics. We also stress the neutrality of information with respect to the physical theories that describe the systems used for its implementation. This view opens the way towards a non-reductive unification of physics: if different physical theories can be reconstructed on the same neutral informational basis, they could be meaningfully compared with no need of searching for reductive links among them. (shrink)

This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac’s work, which, in particular Dirac’s derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg’s earlier work leading him to the discovery of (...) quantum mechanics, which inspired Dirac’s work. I argue that Heisenberg’s and Dirac’s work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D’Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac’s equations from these principles alone, without using the principles of relativity. (shrink)

Spirituality is a topic of recent interest. Mindfulness, for example, a concept derived from the Buddhist tradition, has captivated the imagination of clinicians who package it in convenient intervention programs for patients. Spirituality and religion have been researched with reference to potential health benefits. Spirituality can be conceptualised as the alignment of the individual with the whole, experientially, motivationally and in action. For spirituality to unfold its true potential it is necessary to align this new movement with the mainstream of (...) science, and vice versa. Hence, both a historical review, and a systematic attempt at integration is called for, which we are trying to give here. It is useful to go back to one of the roots: parapsychology. Parapsychology was founded as a counter movement to the rising materialist paradigm in the 19th century. Adopting the methods of the natural sciences, it tried to prove the direct influence of consciousness on matter. After 125 years this mission must be declared unaccomplished. Surveying the database of parapsychological research it is obvious that it will not convince sceptics: Although there are enough exceptional findings, it has in general not been possible to reproduce them in replication experiments. This is, however, a characteristic signature of a category of effects which we call effects of generalised entanglement, predicted by a theoretical model analogous to quantum theory. Using this perspective, parapsychological effects can be understood, and the original aim of the founding fathers can be recovered, as well as a new, systematic understanding of spirituality be gained. Generalised entanglement is a formal and scientific way of explaining spirituality as alignment of an individual with a whole, which, according to the model, inevitably leads to non-local correlations. (shrink)

In a previous paper (Duncan, T.L., Semura, J.S. in Entropy 6:21, 2004) we considered the question, “What underlying property of nature is responsible for the second law?” A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second law. This line of thinking highlights the existence of two independent but coupled sets of laws: Information dynamics and energy dynamics. The distinction helps shed light on certain foundational questions in statistical mechanics. For (...) example, the confusion surrounding previous “derivations” of the second law from energy dynamics can be resolved by noting that such derivations incorporate one or more assumptions that correspond to the loss of information. In this paper we further develop and explore the perspective in which the second law is fundamentally a law of information dynamics. (shrink)

Scholars concerned with the foundations of quantum mechanics (QM) usually think that contextuality (hence nonobjectivity of physical properties, which implies numerous problems and paradoxes) is an unavoidable feature of QM which directly follows from the mathematical apparatus of QM. Based on some previous papers on this issue, we criticize this view and supply a new informal presentation of the extended semantic realism (ESR) model which embodies the formalism of QM into a broader mathematical formalism and reinterprets quantum probabilities as conditional (...) on detection rather than absolute. Because of this reinterpretation a hidden variables theory can be constructed which justifies the assumptions introduced in the ESR model and proves its objectivity. When applied to special cases the ESR model settles long-standing conflicts (it reconciles Bell’s inequalities with QM), provides a general framework in which previous results obtained by other authors (as local interpretations of the GHZ experiment) are recovered and explained, and supports an interpretation of quantum logic which avoids the introduction of the problematic notion of quantum truth. (shrink)

Wallace has recently argued that a number of popular approaches to the measurement problem can’t be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only the unitary-only approaches to the measurement problem are viable. However, the unitary-only approaches face serious epistemic problems which may threaten their viability as solutions, and thus we consider that it remains an urgent outstanding problem to find a viable solution to the measurement problem which can (...) be extended to relativistic quantum mechanics. In this article we seek to understand in general terms what such a thing might look like. We argue that in order to avoid serious epistemic problems, the solution must be a single-world realist approach, and we further argue that any single-world realist approach which is able to reproduce the predictions of relativistic quantum mechanics will most likely have the property that our observable reality does not supervene on dynamical, precisely-defined microscopic beables. Thus we suggest three possible routes for further exploration: observable reality could be approximate and emergent, as in relational quantum mechanics with the addition of cross-perspective links, or observable reality could supervene on beables which are not microscopically defined, as in the consistent histories approach, or observable reality could supervene on beables which are not dynamical, as in Kent’s solution to the Lorentzian classical reality problem. We conclude that once all of these issues are taken into account, the options for a viable solution to the measurement problem are significantly narrowed down. (shrink)

Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of ‘orthodox interpretations,’ which includes QBism, neo-Copenhagen interpretations, and some versions of relational quantum mechanics. We demonstrate that intersubjectivity fails in radical ways in these approaches, and we explain why intersubjectivity matters for empirical confirmation. We take a detailed look at the way in which (...) belief-updating might work in the kind of universe postulated by an orthodox interpretation, and argue that observers in such a universe are unable to escape their own perspective in order to learn about the structure of the set of perspectives that is supposed to make up reality according to these interpretations. We also argue that in some versions of these interpretations it is not even possible to use one’s own relative frequencies for empirical confirmation. Ultimately we conclude that it cannot be rational to believe these sorts of interpretations unless they are supplemented with some observer-independent structure which underwrites intersubjective agreement in at least certain sorts of cases. (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.

Several contemporary interpretations of quantum mechanics use the concept of information as a tool for addressing and explaining the quantum world. In the article, I focus on Zeilinger-Brukner's informational foundations of quantum theory. I propose that with a phenomenological approach—which, unlike most of the contemporary interpretations of quantum mechanics, exceeds the mere dichotomy between realism and anti-realism—we can address the epistemological questions re-opened by IFQT and the parts of the interpretation that are recognized as problematic by its critics. After the (...) phenomenological supplementation IFQT can provide both, ontic and epistemic answer to the question "Why quantum?" As we apply Husserl's concept of the world as our common objective ground to the IFQT explanation, we can make a justifiable step away from the solipsism/subjectivism, which is, according to the critics, the main problem of IFQT. Thus, I propose in conclusion, a phenomenological approach to quantum physics can offer a background for the much needed dialog between realists and anti-realists as well as for a comprehensive contemporary interpretation of the quantum world. (shrink)

According to Zeilinger’s information interpretation of quantum mechanics ‘the distinction between reality and our knowledge of reality, between reality and information, cannot be made. They are in a deep sense indistinguishable’. This is what we call Zeilinger’s thesis. This thesis has been criticized as a lapse into ‘informational immaterialism’ and amounting to nothing more than a tautology. However, we will argue that this criticism is based on a pre-Kantian view of reality, namely metaphysical realism which could be questioned on the (...) basis of Putnam’s arguments. Furthermore, it will be argued that to understand Zeilinger’s thesis one should abandon the pre-Kantian perspective of metaphysical realism and adopt a post-Kantian perspective on the relationship between the mind and the world. (shrink)

QBism is one of the main candidates for an epistemic interpretation of quantum mechanics. According to QBism, the quantum state or the wavefunction represents the subjective degrees of belief of the agent assigning the state. But, although the quantum state is not part of the furniture of the world, quantum mechanics grasps the real via the Born rule which is a consistency condition for the probability assignments of the agent. In this paper, we evaluate the plausibility of recent criticism of (...) QBism. We focus on the consequences of the subjective character of the quantum state, the issue of realism and the problem of the evolution of the quantum state in QBism. In particular, drawing upon Born’s notion of invariance as the mark of the real, it is argued that there is no essential difference between Einstein’s program of ‘the real’ and QBists’ realism. Also, it will be argued that QBism can account for the unitary evolution of the quantum state. (shrink)

We consider probability theories in general. In the first part of the paper, various constraints are imposed and classical probability and quantum theory are recovered as special cases. Quantum theory follows from a set of five reasonable axioms. The key axiom which gives us quantum theory rather than classical probability theory is the continuity axiom, which demands that there exists a continuous reversible transformation between any pair of pure states. In the second part of this paper, we consider in detail (...) how the measurement process works in both the classical and the quantum case. The key differences and similarities are elucidated. It is shown how measurement in the classical case can be given a simple ontological interpretation which is not open to us in the quantum case. On the other hand, it is shown that the measurement process can be treated mathematically in the same way in both theories even to the extent that the equations governing the state update after measurement are identical. The difference between the two cases is seen to be due not to something intrinsic to the measurement process itself but, rather, to the nature of the set of allowed states and, therefore, ultimately to the continuity axiom. (shrink)

Recently, Brukner and Zeilinger 3354) have claimed that the Shannon information is not well defined as a measure of information in quantum mechanics, adducing arguments that seek to show that it is inextricably tied to classical notions of measurement. It is shown here that these arguments do not succeed: the Shannon information does not have problematic ties to classical concepts. In a further argument, Brukner and Zeilinger compare the Shannon information unfavourably to their preferred information measure, I , with regard (...) to the definition of a notion of “total information content.” This argument is found unconvincing and the relationship between individual measures of information and notions of “total information content” investigated. We close by considering the prospects of Zeilinger's Foundational Principle as a foundational principle for quantum mechanics. (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.

Focusing on Shannon information, this article shows that, even on the basis of the same formalism, there may be different interpretations of the concept of information, and that disagreements may be deep enough to lead to very different conclusions about the informational characterization of certain physical situations. On this basis, a pluralist view is argued for, according to which the concept of information is primarily a formal concept that can adopt different interpretations that are not mutually exclusive, but each useful (...) in a different specific context. (shrink)

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics, which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in a game, than (...) the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics. (shrink)

If quantum mechanics is correct and there is a finite upper bound for the speed of causal influences (e.g., the speed of light), then quantum mechanics is complete (i.e., it does not admit a more detailed description in terms of hidden variables). Here I show that the conclusion holds if we replace the assumption of bounded velocity by the assumption that there is a finite upper bound to the memory a finite physical system can store (e.g., the Holevo bound). On (...) the way to this conclusion I first show that, although the quantum violation of an inequality valid for any non-contextual model can be explained with a classical contextual model, the inequality can be promoted to a Bell inequality in which, if the model is contextual, then it must be also non-local. This suggests that there is something non-classical in any contextual explanation of the individual systems, and leads us to the question of which are the minimum resources (and specifically memory) any contextual explanation should consume. (shrink)

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as (...) in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory. (shrink)

We introduce a two-party communication complexity problem in which the probability of success by using a particular strategy allows the parties to detect with certainty whether or not some forbidden communication has taken place. We show that theprobability of success is bounded by nature; any conceivable method which gives a probability of success outside these bounds is impossible. Moreover, any conceivable method to solve the problem which gives a probability success within these bounds is possible in nature. This example suggests (...) that a suitaby chosen set of communication complexity problems could be the basis of an information-theoretic axiomatization of quantum mechanics. (shrink)

Mitra demonstrates that memory erasure can cause the observer to end up in a different sector of the multiverse with a different destiny, events in the future remote to any possible influence of the observer having radically different probabilities. The concept only applies to an observer defined by a structure of information, so cannot apply to the physical bodies of human observers. However, Everett defines the functional identity of the observer as the contents of the memory, a structure of information, (...) thus in principle Mitra's effect would apply. Here it is shown that not only is this very minimal definition of the observer entirely in accord with the subjective experience of identity of human observers, it is also the only possible definition of a transtemporal observer in a no-collapse universe. With respect to human observers, selective elimination of data is not possible due to the distributed manner in which information is stored in the neural network of the brain, but addition of data works on exactly the same principle. Thus, while it would not be possible to alter the destiny of the observer to reduce the probability of unwanted events to background probability, as in the example Mitra uses to demonstrate the principle, it would be possible to increase the probability of desired events. This would appear to verify certain aspects of folklore which otherwise appear entirely mythical and imaginary. (shrink)

Relational quantum mechanics is an interpretation of quantum theory which discards the notions of absolute state of a system, absolute value of its physical quantities, or absolute event. The theory describes only the way systems affect each other in the course of physical interactions. State and physical quantities refer always to the interaction, or the relation, between two systems. Nevertheless, the theory is assumed to be complete. The physical content of quantum theory is understood as expressing the net of relations (...) connecting all different physical systems. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other quantum (...) behaviors, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert space formalism of quantum mechanics as well as the Born probability rule. Our derivation demonstrates the physical foundation of quantum theory. (shrink)

Generally, there are two interpretative approaches to quantum theory: psi-ontic and psi-epistemic. According to the psi-ontic interpretations, quantum theory does/should describe or represent what...

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (shrink)

Hardy’s paradox was originally presented as a demonstration, without inequalities, of the incompatibility between quantum mechanics and the hypothesis of local causality. Equipped with newly developed tools that allow for a quantitative assessment of realism, here we revisit Hardy’s paradox and argue that nonlocal causality is not mandatory for its solution; quantum irrealism suffices.

In this short review I present my personal reflections on Zeilinger–Brukner information interpretation of quantum mechanics.In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically. This review is written in non-physicist friendly manner. Experts (...) actively exploring this interpretation may be interested in the paper as well, as in the comments of “an external observer” who have been monitoring the development of this approach to QM during the last 18 years. The last part of this review is devoted to the general methodology of science with references to views of de Finetti, Wigner, and Peres. (shrink)

In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework covering all events related (...) to the experiment. This approach can be applied to any complex experiment in which statistical data are collected for various experimental settings. (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.

Building on Peres’ idea of “Delayed-choice for entanglement swapping” we show that even the degree to which quantum systems were entangled can be defined after they have been registered and may even not exist any more. This does not arise as a paradox if the quantum state is viewed as just a representative of information. Moreover such a view gives a natural quantification of the complementarity between the measure of information about the input state for teleportation and the amount of (...) entanglement of the resulting swapped entangled state. (shrink)