Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, (...) the concomitant quantum statistics and their entanglement. Here, we analyse the role of indistinguishability and non-individuality in other areas of quantum theory. We start by analysing how a very peculiar use of indistinguishability underlies Feynman’s rules for summing amplitudes in interference phenomena. Next, we study how quantum indistinguishability is underestimated in several topics of debate in the quantum physics literature, such as the Einstein–Podolsky–Rosen argument, Bell’s inequalities and the Bell–Kochen–Specker theorem. Finally, we argue that an ontology of truly indistinguishable entities can serve as a basis for a quantum ontology that can give interesting answers to the interpretational problems of quantum mechanics. We claim that, in addition to superposition, contextuality and entanglement, indistinguishability (understood in a robust ontological sense) is one of the central features of quantum physics. -/- . (shrink)

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than (...) 1. The proposed approach highlights the utility of using a separable basis for constructing the bipartite quantum histories and allows for quantification of their entanglement from the complete set of experimentally measured sequential weak values. We then illustrate the nonclassical nature of entangled histories with the use of Hardy's overlapping interferometers and explain why local hidden variable theories are unable to correctly reproduce all observable quantum outcomes. Our theoretical results elucidate how the composite tensor product structure of multipartite quantum systems is naturally extended across time and clarify the difference between quantum histories viewed as projection operators in the history Hilbert space and those viewed as chain operators and propagators in the standard Hilbert space. (shrink)

Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how separate contextuality scenarios combine into a joint scenario. Under the premise that the the allowed probabilistic models satisfy the No Signalling principle, Foulis and Randall defined the unique possible way to compose two contextuality scenarios. When composing strictly-more than two test spaces, (...) however, a variety of possible composition methods have been conceived. Nevertheless, all these formally-distinct composition methods appear to give rise to observationally equivalent scenarios, in the sense that the different compositions all allow precisely the same sets of classical and quantum probabilistic models. This raises the question of whether this property of invariance-under-composition-method is special to classical and quantum probabilistic models, or if it generalizes to other probabilistic models as well, our particular focus being \ models. \ models are physically important since, when applied to scenarios constructed by a particular composition rule, coincide with the well-defined “Almost Quantum Correlations”. In this work we see that some composition rules, however, give rise to scenarios with inequivalent allowed sets of \ models. We find that the non-trivial dependence of \ models on the choice of composition method is apparently an artifact of failure of those composition rules to capture the orthogonality relations given by the Local Orthogonality principle. We prove that \ models satisfy invariance-under-composition-method for all the constructive compositions protocols which do capture this notion of Local Orthogonality. (shrink)

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of subsets of a (...) set of qubits; in the case of three qubits we find quantum Bell inequalities—necessary conditions for a set of two-qubit states to be the reduced states of a mixed state of three qubits. We conjecture that these conditions are also sufficient. (shrink)

Using different quantum states (e.g., two mode squeezed-state, multipartite GHZ-like-states) as quantum resources, two protocols for "continuous variable (CV) controlled quantum conference" are proposed. These CV protocols for controlled quantum conferences (CQCs) are the first of their kind and can be reduced to CV protocols for various other cryptographic tasks. In the proposed protocols, Charlie is considered the controller, having the power to terminate the protocol at any time and to control the flow of information (...) among the other users by using a parameterised control switch. Based on the information shared by Charlie with the participants of the conference, the control power of Charlie is evaluated and compared to the proposed protocols. The comparison of the efficiency of the proposed protocols has revealed that, under certain constraints, the 4-mode GHZ state-based protocol is more efficient than the two-mode squeezed state-based protocol. The control power Charlie is evaluated for the proposed protocols under certain constraints. A security analysis is also performed, and it is observed that the proposed protocols are secure against a variety of attacks, including but not limited to disturbance attacks, man-in-the-middle attacks, Trojan horse attacks, laser seeding attacks, cloning attacks, beam splitter attacks, and malicious user(s) attacks. (shrink)

According to quantum mechanics, the informational content of isolated systems does not change in time. Considering composite systems, it would be very useful to identify suitable indicators able to quantify the informational content of the single parts and to describe their evolution through balance equations, as it happens in the case of energy. Reasoning on the basic concepts of quantum mechanics, we show that there is an intrinsic quantum information encoded in the coherence of (...) class='Hi'>quantum states. Such information is measured by a function, called here coherent entropy, which turns out to be complementary to the von-Neumann entropy. We show that the total quantum information of multipartite systems is determined by the coherent entropy of the single subsystems plus their mutual information. Interestingly, the coherent entropy is found to be equal to the information conveyed in the future by quantum states, providing a further inspiring interpretation to this quantity. The vision proposed in this paper also suggests a natural and simple definition of an indicator for nonlocal correlations. (shrink)

We start from the assumption that the real valued observables of a quantum system form a Jordan algebra which is equipped with a compatible Lie product characterizing infinitesimal symmetries, and ask whether two such systems can be considered as independent subsystems of a larger system. We show that this is possible if and only if the associator of the Jordan product is a fixed multiple of the associator of the Lie product. In this case it is known that (...) the two products can be combined to an associative product in the Jordan algebra or its complexification, depending on the sign of the multiple. (shrink)

Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is a collection of 33 selected papers from the scientific contributions presented at the 16th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI), held at Ishikawa Prefecture Museum of Art in Kanazawa, Japan, from September 11th to 17th, 2011. The volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a (...) wide range of problems in physics, chemistry, and biology. The breadth and depth of the scientific topics discussed during QSCP-XVI appears in the classification of the contributions in six parts: I. Fundamental Theory II. Molecular Processes III. Molecular Structure IV. Molecular Properties V. Condensed Matter VI. Biosystems. Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is written for advanced graduate students as well as for professionals in theoretical chemical physics and physical chemistry. The book covers current scientific topics in molecular, nano, material, and bio sciences and provides insights into methodological developments and applications of quantum theory in physics, chemistry, and biology that have become feasible at end of 2011. (shrink)

This thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a "clock" runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the regime where (...) class='Hi'>quantum theory and general relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. (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)

Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector? The analogous question for compact quantum systems is raised, and some preliminary results are obtained.

There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability. Out of this discussion has arisen a concept called “permutation invariance” that is asserted to apply to quantum systems. I argue that in fact there is no such invariance, and that the best way to understand the permutation of labels in the symmetrized states is as an exchange of haecceities, rather than as an exchange of essences equivalent to permutation invariance. I argue that (...) the strongest notion of haecceity (i.e., "classical haecceity") does not apply at the quantum level, but that in order to properly account for the need for symmetrization in quantum systems, a weaker kind of haecceity must be involved, which I call quantum haecceity. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the (...) idealisation is removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

Recently a new attempt to go beyond QM was performed in the form of so-called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., the electron field or the neutron field. Averages of quantum observables arise as approximations of averages of classical variables (functionals of “prequantum fields”) with respect to fluctuations of fields. For classical variables given by quadratic functionals of fields, quantum and prequantum averages simply coincide. (...) In this paper we generalize PCSFT to the composite quantum system. The main discovery is that, opposite to a rather common opinion, a composite system can be described by the Cartesian product of state spaces (like in classical physics) and not by the tensor product of them (like in conventional QM). A natural interpretation of the quantum pure state for a composite system is proposed: it is the nondiagonal block in the covariance matrix of the random field describing a composite system. The interpretation of a pure state due to Dirac and von Neumann seems to be an artifact of the conventional mathematical description of micro-systems. PCSFT provides a new possibility for interpretation of entanglement. (shrink)

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered (...) here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories. (shrink)

In this short paper, we propose a special class of quantum systems with implicit quantum uncertainties without any probability structure followed by the dynamical behavior of the systems. When a system is deterministic or random, it does not capture the essence of freedom of choice (FOC), which is the ability to make decisions followed by one’s preferences, free from both deterministic and random outcomes. The proposed special class of quantum systems contains non-deterministic yet non-random (...) outcomes, and so they open the possibility of having FOC within the systems. We also examine examples of such a special class of quantum systems that do not violate the postulates of quantum mechanics. (shrink)

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. (...) We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any (...) version of Copenhagen interpretation would allow. A new approach to classical properties and measurement problem is suggested. A quantum definition of classical states is proposed. (shrink)

There are at least three different notions of degrees of freedom that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the other to the structure of the system and the third to the properties of dynamical orbits. In this paper, definitions and comparison in classical and quantum systems of the tree types of DF are formulated and discussed. In particular, we concentrate (...) on comparison of the number of the so called dynamical DF in a quantum system and its classical model. The comparison involves analyzes of relations between integrability of the classical model, dynamical symmetry and separability of the quantum and the corresponding classical systems and dynamical generation of appropriately defined quantumness. The analyzes is conducted using illustrative typical systems. A conjecture summarizing the observed relation between generation of quantumness by the quantum dynamics and dynamical properties of the classical model is formulated. (shrink)

We use a quantum electrodynamics model, to study the evolution of maximally entangled bipartite states, as well as a maximally entangled tripartite states as a multipartite system. Furthermore, we study the entanglement behaviour of these output states in cavity QED as function of interaction time and the coupling strength. The present study discusses the separability and the entanglement limit of such states after interaction with a cavity QED.

The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the (...) one he calls the “quantum H-theorem,” is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem,” is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: For a “typical” finite family of commuting macroscopic observables, every initial wave function ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψ is close to.. (shrink)

In a previous essay I argued that quantum chaos cannot be exhibited in models of quantum systems within von Neumann's mathematical framework for quantum mechanics, and that it can be exhibited in models within Dirac's formal framework. In this essay, the negative thesis concerning von Neumann's framework is elaborated further by extending it to the case of Hamiltonian operators having a continuous spectrum. The positive thesis concerning Dirac's formal framework is also elaborated further by constructing a (...) chaotic model of an open quantum system in which an entropy measure is shown to approach its maximum value as time goes to infinity. Having such an entropy measure is a characteristic that is closely connected to chaotic behavior in phase space models of classical systems. (shrink)

This paper proposes an extension of Chaitin's halting probability Ω to a measurement operator in an infinite dimensional quantum system. Chaitin's Ω is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent ways to define the program-size complexity H of a given finite binary string s. In the standard way, H is defined as the length of the (...) shortest input string for U to output s. In the other way, the so-called universal probability m is introduced first, and then H is defined as –log2m without reference to the concept of program-size.Mathematically, the statistics of outcomes in a quantum measurement are described by a positive operator-valued measure in the most general setting. Based on the theory of computability structures on a Banach space developed by Pour-El and Richards, we extend the universal probability to an analogue of POVM in an infinite dimensional quantum system, called a universal semi-POVM. We also give another characterization of Chaitin's Ω numbers by universal probabilities. Then, based on this characterization, we propose to define an extension of Ω as a sum of the POVM elements of a universal semi-POVM. The validity of this definition is discussed.In what follows, we introduce an operator version equation image of H in a Hilbert space of infinite dimension using a universal semi-POVM, and study its properties. (shrink)

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrödinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann’s 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, (...) despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics. (shrink)

The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not (...) the conventional logic of Hilbert space, because only finite combinations of prepositions are allowed. (shrink)

In a series of recent papers, Simon Saunders, Fred Muller, and Michael Seevinck have collectively argued, against the folklore, that some nontrivial version of Leibniz’s principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles—fermions, paraparticles, anyons, even bosons—may be weakly discerned by some physical relation. Here I show that their arguments make illegitimate appeal to nonsymmetric, that is, permutation-noninvariant, quantities and that therefore their conclusions do not go through. However, I show that (...) alternative, symmetric quantities may be found to do the required work. I conclude that the Saunders-Muller-Seevinck heterodoxy can be saved. (shrink)

We develop the theory of symmetry for a two-level quantum system in oder to illustrate the main ideas of the general theory of symmetry in quantum theory. It is based on the diffeomorphism of the two-dimensional sphere S 2 onto the space of states ℂP 1 and the isomorphism between the groups Pℳ(2) and SO 3 (ℝ). In particular, rotational invariance leads to the appearance of the spin1/2 in a natural way.

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

Traditionally, there has been a clear distinction between classical systems and quantum systems, particularly in the mathematical theories used to describe them. In our recent work on macroscopic quantum systems, this distinction has become blurred, making a unified mathematical formulation desirable, so as to show up both the similarities and the fundamental differences between quantum and classical systems. This paper serves this purpose, with explicit formulations and a number of examples in the form (...) of superconducting circuit systems. We introduce three classes of physical systems with finite degrees of freedom: classical, standard quantum, and mixed quantum, and present a unified Hilbert space treatment of all three types of system. We consider the classical/quantum divide and the relationship between standard quantum and mixed quantum systems, illustrating the latter with a derivation of a superselection rule in superconducting systems. (shrink)

Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate correspondence with Newtonian gravitation. The results are consistent with known experimental results that indicate the maintenance of the quantum coherence of gravitating systems, as expected through the equivalence principle.

We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to (...) Heq. We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors ψ0 evolve in such a way that ψt is in thermal equilibrium for most times t. This result is closely related to von Neumann’s quantum ergodic theorem of 1929. (shrink)

Spontaneous symmetry breaking in quantum systems, such as ferromagnets, is normally described as degeneracy of the ground state; however, it is well established that this degeneracy only occurs in spatially infinite systems, and even better established that ferromagnets are not spatially infinite. I review this well-known paradox, and consider a popular solution where the symmetry is explicitly broken by some external field which goes to zero in the infinite-volume limit; although this is formally satisfactory, I argue that (...) it must be rejected as a physical explanation of SSB since it fails to reproduce some important features of the phenomenology. Motivated by considerations from the analogous classical system, I argue that SSB in finite systems should be understood in terms of the approximate decoupling of the system's state space into dynamically-isolated sectors, related by a symmetry transformation; I use the formalism of decoherent histories to make this more precise and to quantify the effect, showing that it is more than sufficient to explain SSB in realistic systems and that it goes over in a smooth and natural way to the infinite limit. (shrink)

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates the observations of (...) chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule. (shrink)

We introduce an explicit definition for “hidden correlations” on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the “proper state” of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collection of individual entities between which there exist such hidden correlations. We investigate the significance of these hidden correlation representations (...) within Aerts' creation-discovery approach and in particular their compatibility with the hidden measurement formalism. This leads us to the introduction of the notions of “soft” and “hard” “acts of creation” and to the observation that our approach can be seen as a theory of individuals when it is compared to the standard quantum theory. (shrink)

In a recent paper, a “distance” function, $\cal D$ , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors (...) for simplicity and clarity. Several specific examples are calculated. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models (...) and evaluate their consistency and distinctness. The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (shrink)

An axiomatic foundation of a quantum theory for microsystems in the presence of external fields is developed. The space-time structure is introduced by considering the invariance of the theory under a kinematic invariance group. The formalism is illustrated by the example of charged particles in electromagnetic potentials. In the example, gauge invariance is discussed.

Panmicropsychism is the view that the fundamental physical ingredients of our universe are also its fundamental phenomenal ingredients. Since there is only a limited number of fundamental physical ingredients, panmicropsychism seems to imply that there exists only a small set (palette) of basic phenomenal qualities. How does this limited palette of basic phenomenal qualities give rise to our rich set of experiences? This is known as ‘the palette problem’. One class of solutions to this problem, large-palette solutions, simply denies that (...) the palette is limited. These solutions assume that all types of phenomenal qualities (color, sound, odor, taste, etc., and presumably also types not experienced by humans) were created fully formed at the birth of our universe. On this view, brains evoke conscious experiences by sampling primordial, preexisting phenomenal spaces. My main claim in this paper is that, by analogy with the mathematical description of the fundamental physical ingredients of our universe, which exhibits simplicity, symmetry, and beauty, panmicropsychists should expect the mathematical description of the fundamental phenomenal ingredients of our universe to exhibit similar features. The goal of this paper is to exemplify this claim using what is arguably the simplest of all types of phenomenal qualities—color. Specifically, I utilize phenomenological data on color to construct the maximally symmetric mathematical description of phenomenal color space. I then show that this mathematical description is isomorphic to the mathematical description of two-state quantum systems in a mixed state. Based on this isomorphism, I suggest that color may be the phenomenal dual aspect of two-state quantum systems. (shrink)

Attempts to create a coherent scientific picture of the world as a whole on the basis of quantum physics has sped up at the turn of the millennium. There particularly seem to be expectations that the development of a new kind of quantum mechanics could make it possible to describe both matter and consciousness in one frame of reference (“dual aspect approach”). These ideas are often results of brilliant intuitive visions but as yet not able to produce testable (...) hypotheses. Maybe “wave mechanics” is not very suitable in the study of consciousness from the quantum mechanical point of view. The aim of this article is to show how both the matter and the mind systems can be described with one coherent mathematical model if we assume both space and time to be discrete. (shrink)

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum (...) states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”. (shrink)

The recent renewed interest in the foundation of quantum statistical mechanics and in the dynamics of isolated quantum systems has led to a revival of the old approach by von Neumann to investigate the problem of thermalization only in terms of quantum dynamics in an isolated system [1, 2]. It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed approaches an equilibrium state [3–9]. The underlying (...) idea that a single pure quantum state can fully describe thermal equilibrium has also become much more concrete [10–12]. (shrink)

The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of (...) composite quantum systems. 6. (shrink)

To which ontological category do quantum systems belong? Although we usually speak of particles, it is well known that these peculiar items defy several traditional metaphysical principles. In the present chapter these challenges will be discussed in the light of certain distinctions usually not taken into account in the debate about the ontological nature of quantum systems. On this basis, it will be argued that an ontology of properties without individuals, framed in the algebraic formalism of (...) quantum mechanics, provides adequate answers to the ontological challenges raised by the theory.What kind of item is a quantum system? In the practice of physics it is common to speak of quantum particles, as if they were items of a similar nature to classical items, but obeying different laws of motion. However, as is well known, quantum systems have such peculiar features that they challenge certain ontological principles and categories as understood in traditional metaphysics. In general, these features are analyzed in the context of the so-called problem of indistinguishability, which is a consequence of the particular statistical behavior of quantum systems. But the fact that certain items are “indistinguishable” is not the only difficulty to be overcome in order to elucidate the ontological category of quantum systems. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations (...) of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

In previous work, a non-standard theory of probability was formulated and used to systematize interference effects involving the simplest type of quantum systems. The main result here is a self-contained, non-trivial generalization of that theory to capture interference effects involving a much broader range of quantum systems. The discussion also focuses on interpretive matters having to do with the actual/virtual distinction, non-locality, and conditional probabilities.

A pair of spin-j particles, prepared in a singlet state, move away from each other and are examined by two distant observers. If the latter are able to discriminate between the2j+1 values of a component ofJ, there are pairs of observables whose correlation strongly violates Bell's inequality, for arbitrarily large j. However, if neighboring values are lumped together because of limited instrumental resolution, the observable correlations tend to those predicted by classical mechanics.

Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.

In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic (...) philosophical attitude, although substantially different from the classical one. (shrink)

The traditional formalism of quantum mechanics is mainly used to describe ensembles of identical systems (with a density-operator formalism) or single isolated systems, but is not capable of describing single open quantum objects with many degrees of freedom showing pure-state stochastic dynamical behaviour. In particular, stochastic 'line-migration' as in single-molecule spectroscopy of defect molecules in a molecular matrix is not adequately described. Starting with the Bohr scenario of stochastic quantum jumps (between strict energy eigenstates), we (...) try to incorporate more general pure-state stochastic dynamical behaviour into the quantum mechanical formalism.Probability distributions of (approximately) pure states, arising through the stochastic pure-state dynamics for long times, give rise to appropriate decompositions of thermal density operators. These decompositions of density operators into pure states mediate between quantum mechanics for ensembles of molecules and quantum theory for single molecules (or single dressed quantum objects). We suggest that such decompositions should be consistent with infinite limits (e.g. the Born-Oppenheimer limit for infinite nuclear masses) in the sense that quantum fluctuations (around classical behaviour in the infinite limit) die out asymptotically. (shrink)