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)

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)

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...

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 (...) forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system. (shrink)

We discuss foundational issues of quantum information biology —one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from “traditional quantum biophysics”. The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (...) is the most natural interpretation of QIB. Biologically QIB is based on two principles: adaptivity; openness. These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems. (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)

Recently, Brukner and Zeilinger have presented a number of arguments suggesting that the Shannon information is not well defined as a measure of information in quantum mechanics. If established, this result would be highly significant, as the Shannon information is fundamental to the way we think about information not only in classical but also in quantum information theory. On consideration, however, these arguments are found unsuccessful; I go on to suggest how they might be arising as a consequence of Zeilinger`s (...) proposed foundational principle for quantum mechanics. (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)

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)

Bohr’s interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr’s influence, in the pre-war period of 1927–1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie’s had no reasonable foundation. But Bohr’s interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually (...) wide scope, on the nature and future course of explanations in the sciences (and not only the physical sciences). If it must be judged a failure today, it is not because of any internal inconsistency. (shrink)

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)

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)

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)

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 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)

We formalize the notion of isolated objects, and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless (...) elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects. (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)

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)

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)

With the example of a Stern–Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse—for example, the singleness (or mutual exclusivity) of outcomes. This is done by inserting a quantum two-state system (an ancilla) in each path, capable of responding to the passage of the atom, and thus acting as a virtual detector. We then consider real measurements on the compound system of atomic spin and two (...) ancillae. Nondestructive measurements of a set of compatible joint observables can be performed, one for a superposition and others for collapse properties. A novel perspective is given as to why, within unitary quantum theory, ordinary measurements are blind to such superpositions. Implications for the theory of measurement are discussed. (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)

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)

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for (...) the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities “out there”. (shrink)

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and (...) from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed. (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)

The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of Quantum Theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative case studies, I take Clifton's, Bub's and (...) Halvorson's characterization theorem and Popescu's and Rohrlich's toy models, and their explanatory contribution with respect to quantum nonlocality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of quantum nonlocality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory. (shrink)

Brukner and Dakić proposed a very simple axiom system as a foundation for quantum theory. It implies the qubit and quantum entanglement. Because this axiom system aims at the core of our understanding of nature, it must be brought to the forum of the philosophy of nature. For philosophical reasons, a completely denied champion of quantum theory, imaginarity i, is added into this axiom system. In relation to Bell’s inequality, this leads to a deeper ‘philosophical’ understanding of quantum nature based (...) on qubits and entanglement. Both opens a way as well as one can get to the fundamental Schrödinger equation of quantum mechanics with the help of a complex valued Brownian motion. (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)

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)

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)

In modern science, established by the scientific revolution in 16th and 17th century, the scientific observation process is understood as a process where the observer directly grasps Nature as the observed and scientific mathematical formulation is understood as a direct description of reality. Husserl criticized this lack of distinction between method and the object of investigation in modern science and emphasized the importance of phenomena in the observation process. A similar approach was used by Bohr in his interpretation of quantum (...) experiments that seemed inexplicable from the modern science point of view. Many contemporary interpretations of quantum mechanics follow Bohr’s opposition to the realism of modern science. Among them is informational foundations of quantum theory that connects parts of his interpretation with the latest quantum experiments, but due to the complexity and individuality of Bohr’s interpretation, its philosophical consistency is mostly lost. In IFQT there is no direct connection between information and the observed. This ambiguous ontic status of information is often criticised, however, it can be solved by supplementation with Husserl’s philosophical understanding of the observation process. If Husserl’s definition of the relationship between the thing and the phenomenon is transmitted to the relationship between the observed and information in IFQT information can be understood as the direct answer to the question about the observed and thereby the observer’s only knowledge about it. This helps to reject the main criticism of IFQT and to additionally support its explanations of quantum phenomena. (shrink)

In this work I argue for the existence of an ontological state in which no entity in it can be more basic than the others in such a state. This is used to provide conceptual justification for a method that is applied to obtain the Schr\"{o}dinger equation, the Klein-Gordon equation, and the Klein-Gordon equation for a particle in an electromagnetic field. Additionally, it is argued that the existence of such state is incompatible with indirect realism; and the discussion suggests that (...) a panexeperientialist view is a straightforward means to embrace it. (shrink)