Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck-Einstein relation (...) between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex. (shrink)

Quantum–mechanical systems may be understood in terms of information. When they interact, they modify the information they carry or represent in two, and only two, ways: by selecting a part of the initial amount of (potential) information and by sharing information with other systems. As a consequence, quantum systems are informationally shielded. These features are shown to be general features of nature. In particular, it is shown that matter arises from quantum–mechanical processes through (...) the constitution of larger ensembles that share some information while living organisms make use of a special form of information selection. (shrink)

Information may be extracted from a quantum–mechanical system only by means of inference. For this reason, the observer, although not required as such for obtaining an eigenstate of the measured observable on a given system, is necessary for obtaining information.

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)

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a (...) theorem that any such theory naturally gives rise to a ''weak effect algebra'' when outcomes having the same probability in all states are identified and in the introduction of a notion of ''operation algebra'' that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ''inside view,'' i.e., for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ''geometric'' picture (''outside view'') coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ''objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ''geometric'' conception of physics. (shrink)

A recent no-go theorem (Frauchiger and Renner in Nat Commun 9(1):3711, 2018) establishes a contradiction from a specific application of quantum theory to a multi- agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio (in: Selinger P, Chiribella G (eds) Proceedings of the 15th international conference on quantum physics and logic (QPL 2018). EPTCS 287, Open Publishing (...) Association, Waterloo, 2018), in which they claim that it shows the “[i]nadequacy of modal logic in quantum settings” (ibid.). In this paper, we will offer a significantly extended and refined reconstruction of the theorem in multi-agent modal logic. We will then show that a thorough reconstruction of the proof as given by Frauchiger and Renner requires the reflexivity of access relations (system T). However, a stronger theorem is possible that already follows in serial frames, and hence also holds in systems of doxastic logic (such as KD45). After proving this, we will discuss the general implications for different interpretations of quantum probabilities as well as several options for dealing with the result. (shrink)

The surprising aspects of quantum information are due to two distinctly non-classical features of the quantum world: first, different quantum states need not be orthogonal and, second, quantum states may be entangled. Non-orthogonality leads to the blurring of classical distinctions. On the other hand, entanglement leads via non-locality to teleportation and other ``entanglement-assisted'' forms of communication that go beyond what is classically possible. In this article we attempt to understand these new possibilities via an analysis (...) of the significance of entanglement for the basic physical concepts of a ``particle'' and a ``localized physical system''. Classical particles can be individuated on the basis of qualitative differences in their sets of properties. But in entangled states the ``particle labels'' of the quantum formalism usually do not pick out such sets of individuating particle properties. It is sometimes nevertheless possible to think in terms of individual particles, which may be localized; but we argue that in general the structure of quantum mechanics is at odds with such a particle interpretation. This finally leads us to the conclusion that quantum mechanics is best seen as not belonging to the category of space-time theories, in which physical quantities are functions on space-time points. The resulting picture of the quantum world is relevant for our understanding of the way in which quantum theory is non-local, and it sheds light on the novel aspects of quantum information. (shrink)

Some physicists seem to believe that quantum information theory requires a new concept of information (Jozsa, 1998, Quantum information and its properties. In: Hoi-Kwong Lo, S. Popescu, T. Spiller (Eds.), Introduction to Quantum Computation and Information, World Scientific, Singapore, (pp. 49-75); Deutsch & Hayden, 1999, Information flow in entangled quantum subsystems, preprint quant-ph/9906007). I will argue that no new concept is necessary. Shannon's concept of information is sufficient for quantum (...) information theory. Properties that are cited to contrast quantum information and classical information (i.e., Shannon information) actually point to differences in our ability to manipulate, access, and transfer information depending on whether quantum systems, opposed to classical systems, are used in a communication system. I also demonstrate that conceptually puzzling phenomena in quantum information theory, such as dense coding, teleportation, and Schumacher coding, all of which are cited as evidence that a new concept of information is required, do not have to be regarded as such. (shrink)

We shall draw an affirmative answer to the question posed in the title. The key point will be a quantum description of physical reality. Once fixed at ontic level two basic elements, namely the laws of physics and the matter, we argue that the underlying physical reality emerges from the interconnection between these two elements. We consider any physical process, including measurement, modeled by unitary evolution. In this context, we will deduce quantum random- ness as a consequence of (...) inclusion of the observer into the quantum system. The global picture of the universe is in a sense deterministic, but from our own local perspective (as part of the system) we perceive quantum mechanical randomness. Then, the notion of "information" turns out to be a derivative concept. (shrink)

Some physicists seem to believe that quantum information theory requires a new concept of information , Introduction to Quantum Computation and Information, World Scientific, Singapore, ; Deutsch & Hayden, 1999, Information flow in entangled quantum subsystems, preprint quant-ph/9906007). I will argue that no new concept is necessary. Shannon's concept of information is sufficient for quantum information theory. Properties that are cited to contrast quantum information and classical information (...) actually point to differences in our ability to manipulate, access, and transfer information depending on whether quantum systems, opposed to classical systems, are used in a communication system. I also demonstrate that conceptually puzzling phenomena in quantum information theory, such as dense coding, teleportation, and Schumacher coding, all of which are cited as evidence that a new concept of information is required, do not have to be regarded as such. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary (...) particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

Several novel approaches have been proposed to resolve the problem of time by relating it to change. We argue using quantum information theory that the Hamiltonian constraint in quantum gravity cannot probe change, so it cannot be used to obtain a meaningful notion of time. This is due to the absence of quantum Fisher information with respect to the quantum Hamiltonian of a time-reparametization invariant system. We also observe that the inability of this (...) Hamiltonian to probe change can be related to its inability to discriminate between states of such a system. However, if the time-reparametization symmetry is spontaneously broken due to the formation of quantum cosmological time crystals, these problems can be resolved, and it is possible for time to emerge in quantum gravity. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and (...) a qubit. The course of time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and (...) a qubit. The course of time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latters. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in (...) it (a wave function describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as (...) a statistical ensemble after measurement. Quantum in-variance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (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 (...) class='Hi'>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)

Summary Proposed by Einstein, Podolsky, and Rosen (EPR) in 1935, the entangled state has played a central part in exploring the foundation of quantum mechanics. At the end of the twentieth century, however, some physicists and mathematicians set aside the epistemological debates associated with EPR and turned it from a philosophical puzzle into practical resources for information processing. This paper examines the origin of what is known as quantum information. Scientists had considered making quantum computers (...) and employing entanglement in communications for a long time. But the real breakthrough only occurred in the 1980s when they shifted focus from general-purpose systems such as Turing machines to algorithms and protocols that solved particular problems, including quantum factorization, quantum search, superdense code, and teleportation. Key to their development was two groups of mathematical manipulations and deformations of entanglement—quantum parallelism and ‘feedback EPR’—that served as conceptual templates. The early success of quantum parallelism and feedback EPR was owed to the idealized formalism of entanglement researchers had prepared for philosophical discussions. Yet, such idealization is difficult to hold when the physical implementation of quantum information processors is at stake. A major challenge for today's quantum information scientists and engineers is thus to move from Einstein et al.'s well-defined scenarios into realistic models. (shrink)

We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.

El presente artículo busca ofrecer un análisis conceptual de la noción de información, a partir del modo en que es definida por las teorías formales de Claude Shannon y de Benjamin Schumacher. Contra la postura según la cual existen dos tipos de información de naturalezas diferentes, una información clásica y una información cuántica, aquí argumentamos que no hay razones suficientes para sostener la existencia de la información cuántica como un nuevo tipo sustancialmente distinto de información. Afirmamos así que existe un (...) único tipo de información que puede ser codificado de diversas maneras, en particular, mediante sistemas clásicos o sistemas cuánticos. Esta posición nos conducirá a concebir un concepto unificado y abstracto de información, en un contexto donde la teoría de Shannon resulta neutral e independiente de las teorías físicas utilizadas para describir las partes involucradas en el proceso de transmitir información, y la teoría de Schumacher no define un nuevo tipo de entidad informacional, sino una manera alternativa de codificar la información mediante estados cuánticos. The aim of this article is to offer a conceptual analysis of the notion of information, on the basis of the way in which it is defined by the theories of Claude Shannon and of Benjamin Schumacher. Against the position according to which there are two kinds of information of different natures, a classical information and a quantum information, here we argue that there are not sufficient reasons to maintain the existence of quantum information as a new and substantially different kind of information. So we claim that there is only one kind of information, which can be encoded in different ways, in particular, by means of classical or quantum systems. This position will lead us to conceive an unified and abstract concept of information in a context where Shannon's theory is neutral and independent from the physical theories used to describe the stages involved in the process of transmitting information, and Schumacher's theory does not define a new kind of informational entity, but a alternative way of coding information by means of quantum states. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of (...) a bit. The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

One can construct a mapping between Hilbert space and the class of all logic if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. Thus that (...) mapping establishes a fundamentally philosophical correspondence between the physical world and universal logic by the meditation of a special and fundamental structure, that of Hilbert space, and therefore, between quantum mechanics and logic by mathematics. Furthermore, Hilbert space can be interpreted as the free variable of "quantum information" and any point in it, as a value of the same variable as "bound" already axiom of choice. (shrink)

We propose a sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves. The algebraic representation of a quantum observable structure in the relational local terms of sheaf theory effectuates a semantic transition from the axiomatic set-theoretic context of orthocomplemented partially ordered sets, la Birkhoff and Von Neumann, to the categorical topos-theoretic context of Boolean information sieves, la Grothendieck. The representation schema is based on the existence of a categorical adjunction, (...) which is used as a theoretical platform for the development of a functorial formulation of information transfer, between quantum observables and Boolean localisation devices in typical quantum measurement situations. We also establish precise criteria of integrability and invariance of quantum information transfer by cohomological means. (shrink)

We review some techniques and notions for quantum information theory. It is shown that the dynamical entropies is discussed and some numerical computations of these entropies are carried for several states.

Given a quantum system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs with vertices representing subsystems and edges representing mutual information between subsystems. The second step is to deform the adjacency matrices of (...) the information graphs to that of a low-dimensional lattice using the graph flow equations introduced in the paper. The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze two information graph flows with geometric attractors and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to quantum gravity in which the geometry emerges directly from a quantum state due to the flow of the information graphs. (shrink)

Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one’s system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the ‘apparent’ collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near (...) future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard. r 2007 Elsevier Ltd. All rights reserved. (shrink)

Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states do not describe an absolute property of a system but rather a relationship between systems. There have recently been some criticisms of RQM pertaining to issues around intersubjectivity. In this article, we show how RQM can address these criticisms by adding a new postulate which requires that all of the information possessed by a certain observer is stored in (...) physical variables of that observer and thus is accessible by measurement to other observers. This makes it possible for observers to reach intersubjective agreement about quantum events that have occurred in the past. We suggest a possible ontology for a version of RQM employing this postulate; this ontology upholds the principle that quantum states are always relational, but it also postulates a set of quantum events that are not strictly relational. We show that the new postulate helps address the preferred basis problem in RQM. (shrink)

We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a (...) remaining open question about nonlocality and bit commitment. (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)

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the (...) objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere. (shrink)

SummaryUnder the assumption of the materialistic‐mechanistic ontology implicit in classical physics, quantum theory as interpreted through Niels Bohr's epistemology of complementarity is not formally objective; i. e., it is not informative of the state of physical systems independent of particular phenomenal manifestations of them. However, an analysis of the notion of the “physical system”, in theory, as experienced, and as existing “in‐itself”, reveals that if the older ontology is replaced, quantum mechanics through complementarity becomes formally objective, points (...) the way toward a new ontology based on the notion of the power to structure interaction between systems, and provides new insights into the relations between theory, observation, and the natural world. (shrink)

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of (...) “the classical” from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence. (shrink)

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.

This book offers a thorough technical elaboration and philosophical defense of an objectivist informational interpretation of quantum mechanics according to which its novel content is located in its kinematical framework, that is, in how the theory describes systems independently of the specifics of their dynamics. -/- It will be of interest to researchers and students in the philosophy of physics and in theoretical physics with an interest in the foundations of quantum mechanics. Additionally, parts of the book may (...) be used as the basis for courses introducing non-physics majors to quantum mechanics, or for self-study by those outside of the university with an interest in quantum mechanics. (shrink)

Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell’s inequality delimiting local - behavior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to figure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly (...) recognized by physicists and philosophers as intimately related to the foundations of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The significance of the relationship between mechanics and information became even clearer with Leo Szilard’s analysis of James Clerk Maxwell’s infamous demon thought experiment. Here, in addition to examining both entanglement and quantum information and their relationship, I endeavor to critically assess the influence of the study of these subjects on the interpretation of quantum theory. (shrink)

A remarkable theorem by Clifton, Bub and Halvorson (2003) (CBH) characterizes quantum theory in terms of information--theoretic principles. According to Bub (2004, 2005) the philosophical significance of the theorem is that quantum theory should be regarded as a ``principle'' theory about (quantum) information rather than a ``constructive'' theory about the dynamics of quantum systems. Here we criticize Bub's principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is (...) no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner--type) thought experiment that we argue demonstrates that quantum mechanics on the information--theoretic approach is incomplete. (shrink)

This is a basically expository article, with some new observations, tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.

The monistic worldview aims at a uniform description of nature based on scientific models. Quantum physical systems are mutually part of the other quantum physical systems. An aperture distributes the subsystems and the wave front in all possible ways. The system only takes one of the possible paths, as measurements show. Conclusion from Bell's theorem: Before the quantum physical measurement, there is no point-like location in the universe where all the information that explains the measurement (...) is available. Distributed information is possible. Movement of the particle and measuring process are deterministic. The oscillation between location uncertainty and momentum uncertainty leads photons to determine their own location at short intervals. The uncertainty principle focuses the systems. The fields of the surrounding matter influence the location of the new formation. The effect of all fields is based on a common mechanism. (shrink)

Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state. The general formula developed there for the best-guess density operator $\hat \rho$ was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumD H of strong equilibrium density operators. In Part II mathematical evaluation of $\hat \rho$ is completed after an epistemological analysis which leads first to the discretization (...) ofD H and then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions. Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized. (shrink)

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to classical constraints, based on a question-and-answer procedure. The problem is posed from a particular batch of queries while the constraints are represented by the truth table of a set of Boolean functions. The Bayesian inference technique consists in assigning a probability (...) distribution within a real-valued probability space to the joint set of queries in order to satisfy the constraints. The initial query batch is not unique and alternative batches can be considered at will. They are enabled mechanically from the initial batch, quite simply by transcribing the probability space into an auxiliary Hilbert space. It turns out that this sole procedure leads to exactly rediscover the standard quantum information theory and thus provides an information-theoretic rationale to its technical rules. In this framework, the great challenges of quantum mechanics become simple platitudes: Why is the theory probabilistic? Why is the theory linear? Where does the Hilbert space come from? In addition, most of the paradoxes, such as uncertainty principle, entanglement, contextuality, nonsignaling correlation, measurement problem, etc., become straightforward features. In the end, our major conclusion is that quantum information is nothing but classical information processed by a mature form of Bayesian inference technique and, as such, consubstantial with Aristotelian logic. (shrink)

The Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics. On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and (...) principles of quantum physics. The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics. The lectures were delivered at the level of PhD students. (shrink)

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum (...) class='Hi'>system and its inseparable thermal bath, formally “entangled” like an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions. (shrink)

We present a novel spontaneous collapse model where size is no longer the property of a physical system which determines its rate of collapse. Instead, we argue that the rate of spontaneous localization should depend on a system’s quantum Integrated Information, a novel physical property which describes a system’s capacity to act like a quantum observer. We introduce quantum Integrated Information, present our QII collapse model and briefly explain how it may be (...) experimentally tested against quantum theory. (shrink)

Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this (...) limitation we demonstrate that such systems exhibit a number of features, such as randomness, no-cloning, and non-commutativity, which are peculiarities attributed to quantum mechanics (QM). After demonstrating many astonishing parallels to quantum behavior, we postulate an interpretation of quantum physics as the physics of systems with a single degree of freedom. We then show how a number of other quantum conundrum can be understood by considering the informational properties of the systems and also resolve the EPR paradox. In the present work, we assume that the formalism of the QM is correct and well-supported by experimental verification and concentrate on the interpretational aspects of the theory. (shrink)

When the state of a physical system is not fully determined by available data, it should be possible nevertheless to make a systematic guess concerning the unknown state by applying the principles of information theory. The resulting theoretical blend of informational and mechanical constructs should then constitute a modern structure for statistical physics. Such a program has been attempted by a number of authors, most notably Jaynes, with seeming success. However, we demonstrated in a recent publication that the (...) standard list of so-called “mutually exclusive and exhaustive” quantum states that is commonly employed by these authors is in fact not exhaustive. It follows that the information-theoretic foundations of quantum statistics must be reformulated. The present paper discusses the fundamental problems involved and establishes a format for the correct application of information theory to quantum mechanical situations. (shrink)

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations (...) on an experimenter's ability to perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard non-relativistic quantum theory and classical relativistic field theory. (shrink)

A quantum state represents neither properties of a physical system nor anyone's knowledge of its properties. The important question is not what quantum states represent but how they are used as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is (...) the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere. (shrink)

Because intelligent agents employ physically embodied cognitive systems to reason about the world, their cognitive abilities are constrained by the laws of physics. Scientists have used digital computers to develop and validate theories of physically embodied cognition. Computational theories of intelligence have advanced our understanding of the nature of intelligence and have yielded practically useful systems exhibiting some degree of intelligence. However, the view of cognition as algorithms running on digital computers rests on implicit assumptions about the physical world that (...) are incorrect. Recently, the view is emerging of computing systems as goal-directed agents, evolving during problem solving toward improved world models and better task performance. A full realization of this vision requires a new logic for computing that incorporates learning from experience as an intrinsic part of the logic, and that permits full exploitation of the quantum nature of the physical world. This paper proposes a theory of physically embodied cognitive agents founded upon first-order logic, Bayesian decision theory, and quantum physics. An abstract architecture for a physically embodied cognitive agent is presented. The cognitive aspect is represented as a Bayesian decision theoretic agent; the physical aspect is represented as a quantum process; and these aspects are related through von Neumann’s principle of psycho-physical parallelism. Alternative metaphysical positions regarding the meaning of quantum probabilities and the role of efficacious choices by agents are discussed in relation to the abstract agent architecture. The concepts are illustrated with an extended example from the domain of science fiction. (shrink)

From the structure of quantum dynamics for closed and open systems, we describe several general results about information flow between interacting systems, which can be expressed in diagrammatic form. Conditions on information flow (e.g., that no information is transferred from system A to system B) imply that the overall dynamical evolution has a particular structure. We also remark that one simple type of two-qubit interaction, the unitary CNOT gate, cannot be represented by local operations (...) and a single simultaneous information exchange. (shrink)