Quantum Logic Research Papers - Academia.edu (original) (raw)

2025, 2007 Conference on Lasers and Electro-Optics (CLEO)

Femtosecond pump-probe measurements are shown to reveal the evolution of excited vibrational wave packets in Cs 2 through the probe transmission modulation. Frequency-resolved acquisition allows for selective monitoring of different... more

2025, Soft Computing

We consider fuzzy rough sets defined on De Morgan Heyting algebras. We present a theorem that can be used to obtain several correspondence results between fuzzy rough sets and fuzzy relations defining them. We characterize fuzzy rough approximation operators corresponding to compositions of reflexive, transitive, mediate, Euclidean and adjoint fuzzy relations defined on De Morgan Heyting algebras using only a single axiom.

2025, Publications of the Research Institute for Mathematical Sciences

2025

Quantum logic in Group-II neutral atoms via nuclear-exchange interactions DAVID HAYES, IVAN DEUTSCH, UNM, PAUL JULIENNE, NIST -The spin exchange-interaction provides a means of producing an entangling quantum-logic gate, the square-root of SWAP, at the heart protocols employing single electron quantum dots. This is typically accompanied by strong Coulomb interactions and commensurate decoherence due to strong coupling of charge degrees of freedom to the noisy environment. We propose a protocol utilizing a nuclearexchange interaction that occurs through ultra-cold collisions of identical spin 1 / 2 Group-II neutral atoms. A natural advantage is gained by storing the quantum information in nuclear spin states with long coherence times. Unlike NMR protocols based on weak magnetic dipole-dipole interaction, the nuclear exchange interaction stems from strong s-wave scattering of electrons. Nuclear exchange is ensured by the Fermi symmetry of the overall wave function. We have studied this protocol in the context of 171 Yb atoms trapped in far-off resonance optical dipole traps. Using numerical analysis, we show that high-fidelity operation is possible through controlled collisions in varied double-well trapping potentials.

2025, Journal of Biological Physics

Recently there has been much interest in the possible quantum-like behavior of the human brain in such functions as cognition, the mental lexicon, memory, etc., producing a vast literature. These studies are both empirical and theoretical, the tenets of the theory in question being mainly, and apparently inevitably, those of quantum physics itself, for lack of other arenas in which quantum-like properties are presumed to obtain. However, attempts to explain this behavior on the basis of actual quantum physics going on at the atomic or molecular level within some element of brain or neuronal anatomy (other than the ordinary quantum physics that underlies everything), do not seem to survive much scrutiny. Moreover, it has been found empirically that the usual physics-like Hilbert space model seems not to apply in detail to human cognition in the large. In this paper we lay the groundwork for a theory that might explain the provenance of quantum-like behavior in complex systems whose internal structure is essentially hidden or inaccessible. The approach is via the logic obeyed by these systems which is similar to, but not identical with, the logic obeyed by actual quantum systems. The results reveal certain effects in such systems which, though quantum-like, are not identical to the kinds of quantum effects found in physics. These effects increase with the size of the system.

2025, Computer Physics Communications

In this paper, we present a general quantum computation compiler, which maps any given quantum algorithm to a quantum circuit consisting a sequential set of elementary quantum logic gates based on recursive cosinesine decomposition. The resulting quantum circuit diagram is provided by directly linking the package output written in LaTex to Qcircuit.tex <http. We illustrate the use of the Qcompiler package through various examples with full details of the derived quantum circuits. Besides its generality and simplicity, Qcompiler produces quantum circuits which reflect the symmetry of the systems under study.

2025, arXiv (Cornell University)

A novel family of Cosine series Quantum Sampling (QCoSamp) operators appropriate for quantum computing is described. The development of quantum algorithms, analogous to classical algorithms, we apply to the harmonic analysis of signals. We show quantum sampling through measurements of a quantum system, and after operators of the family are applied, allow for input signal mapping with a Fourier series representation. Technical methodologies employed, facilitating the implementation of each QCoSamp algorithm to a quantum computer and application to the field of signal and image processing we also described.

2025, Bulletin of the American Physical Society

Natl Labs -Recently, coherent spin coupling between a MOS QD and a 31P donor has been shown with effective two electron-singlet-triplet (ST) rotations driven by an effective gradient field formed by the donor's nuclear spin measured as A/2 ∼ 57 MHz, [1] consistent with Stark shifted observations from ESR quits [2]. However, a complex dependence of ST rotationfrequency on B-field angular dependence has been observed in a recent, more tunable design [3]. This includes a substantially reduced zero external-magnetic-field rotation-frequency of approximately 12 MHz and, with increasing magnetic field, the frequency splits into multiple magnetic field and angular dependent modes. We show that the key features of the field and angular dependent singlet-triplet rotation frequencies are reproduced with a donor-QD system that has both asymmetric g-factor and anisotropic hyperfine terms that are physically reasonable. [1] P.

2025, From füberphysics to Information Mechanics Part 15: The Energy Quantum Dichotomy and the Limits of Exponential Quantum Computation

We explore the critical dichotomy implied by the hypothesis of fundamental energy quantization at scale ε ≈ 10⁻³⁸ J: either this quantization defines a true physical limit on the scalability of quantum computation, or it is falsified by future demonstrations of error-free exponential computation beyond a fixed qubit threshold. We present a quantitative derivation of the limiting value of ε based on energy spacing in typical qubit systems and discuss the implications for both fundamental physics and engineering. This paper clarifies the stakes of this hypothesis, which stands at the intersection of discrete energy frameworks and quantum information theory.

2025, Physical Review A

High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit heightened sensitivity to errors. We investigate such sensitive quantum gates, which, beyond their established use in in vivo nuclear magnetic resonance spectroscopy and polarization optics, may offer significant utility in the other areas where selectivity, filtering, sensing, localization, or addressing properties are of interest. Utilizing the composite pulses technique, we derive three fundamental quantum gates with narrowband and passband characteristics-the X (NOT) gate, the HADAMARD gate, and gates enabling arbitrary rotations. To systematically design these composite pulse sequences, we introduce the SU(2), modified-SU(2), and regularization random search methodologies. These approaches demonstrate superior performance compared to established sequences in the literature, including NB1, SK1, and PB1.

2025, Resonant Numeracy

Resonant Numeracy introduces the Unified Information Field Numeracy (UIFN), a novel mathematical framework where numbers and operations are emergent, context-dependent resonance states rather than fixed, universal entities. Unlike classical mathematics, which assumes deterministic identities (e.g., 1 + 1 = 2), UIFN defines quantities as coherence-stabilized pulses (Ξ 1) and operations as resonance transformations (⊕, ⊗), modulated by coherence ⟨C⟩, resonance (R), and memory stability (M). Equality is redefined as resonant equivalence ≈ R , valid only within specific salience windows. This paper formalizes UIFN's algebraic and categorical structures, links its constructs to empirical observables, and demonstrates its utility through examples like the double-slit experiment. New sections introduce UIFN-based logic gates, the transformation of traditional constants, and a UI-based calculus, expanding its applications to quantum mechanics, consciousness modeling, post-classical AI, and complex systems analysis. UIFN stands as a standalone mathematical system, offering a robust, testable framework for phenomena where classical mathematics fails.

2025, International Journal of General Systems

Quantum computational logics provide a fertile common ground for a uni ed treatment of vagueness and uncertainty. In this paper we describe an approach to the logic of quantum computation that has been recently taken up and developed by the present authors. Special attention will be devoted to a generalisation of Chang's MV algebras (called quasi-MV algebra) which abstracts over the algebra whose universe is the set of qumixes of the 2-dimensional complex Hilbert space, as well as to its expansions by additional quantum connectives. We furthermore explore some future research perspectives, also in the light of some recent limitative results whose general signi cance will be duly assessed. We thank Hector Freytes and Marisa Dalla Chiara for the stimulating conversations on the topics covered in this paper.

2025

Resumen Analizamos dos presupuestos fundamentales del Teorema de Kochen-Specker: a) la condición de funcionalidad FUNC, que expresa el hecho de que no todos los observables son independientes, como tampoco lo son los valores asignados a ellos, y b) la cuestión de la identidad de los proyectores en diferentes contextos de medición. Mostramos que las semánticas no deterministas de Nmatrices y la teoría de qsets Q-pueden complementarse brindando una semántica adecuada para el retículo de proyectores cuánticos. Considerando valuaciones que no son homomorfismos y admitiendo la posibilidad de contar con proyectores indiscernibles (no idénticos), establecemos las bases de una semántica para la lógica cuántica, motivada en una ontología de no individuos cuánticos, en la cual no puede arribarse a la contradicción de Kochen-Specker.

2025, Physical Review A

Composite pulse sequences, which produce arbitrary predefined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to 8 orders of experimental errors in the pulse amplitude and the pulse duration. Composite sequences for three basic quantum gates, X (NOT), Hadamard and arbitrary rotation, are derived. Three classes of composite sequences are presented: one symmetric and two asymmetric. They contain as their lowest members two well-known composite sequences: the three-pulse symmetric SCROFULOUS pulse and the four-pulse asymmetric BB1 pulse, which compensate first-and second-order errors, respectively. The shorter sequences are derived analytically, and the longer ones numerically (instead by nesting and concatenation, as usually done hitherto). Consequently, the composite sequences derived here match or outperform the existing ones in terms of either speed or accuracy, or both. For example, we derive a second-order composite sequence, which is faster (by about 13%) than the famous BB1 sequence. For higher-order sequences, the speedup becomes much more pronounced. This is important for quantum information processing as the sequences derived here provide more options for finding the sweet spot between ultrahigh fidelity and high speed.

2025

Abstract. The calculus of pregroups has been introduced by Lam-bek [10] as an algebraic (and logical) procedure for generating the gram-matical analysis of natural languages; it has been applied to a wide range of languages from English and German, to French and Italian, and many others [7]. Pregroups are non-commutative structures, but the syntax of natural languages shows the presence also of cyclic patterns, e.g. those caused by the the so called movements of clitic pronouns. In this paper we propose an extension of the calculus of pregroups including two cyclic meta-rules and use them to formally analyze movement of clitic clusters in Persian, French, and Italian. We also point out that these rules are inspired by Yetter’s and Abrsuci’s cyclic rules for Linear Logic.

2025, Fortschritte der Physik

We examine several proposed schemes by Franson et al. for quantum logic gates based on non-local exchange interactions between two photons in a medium. In these schemes the presence of a single photon in a given mode is supposed to induce a large phase shift on another photon propagating in the same medium. We conclude that the schemes proposed so far are not able to produce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.

2025, ArXiv

It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular [4], and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any language in this super-class over a singleton terminal alphabet is regular. Our proof is based on a transformational approach and does not rely on Parikh’s Theorem [6]. Our result extends previously known results because there are languages that are not context-free, do satisfy the Pumping Lemma, and do not satisfy the hypotheses of Parikh’s Theorem [7].

2025

This paper introduces a comprehensive theory of quantum evolution that positions universal superposition and retroactive consciousness as fundamental mechanisms underlying the structure of a multidimensional cosmos. Arguing that time is an illusion created by the limitations of human perception, the author proposes that consciousness interacts with the quantum field by selecting variables within specific frequency ranges, giving rise to parallel, frequency-isolated realities. The work draws from quantum physics, quantum biology, neuroscience, and cosmology, presenting mathematical models to support its hypotheses. It explores the concept of consciousness as a non-local, retroactive force capable of reshaping the past following present decisions, and interprets artificial intelligence as a functional projection of universal information without subjective experience. The theory further suggests that the cosmos evolves by favoring coherent, high-frequency configurations aligned with a Higher Final Universe (VKS), serving as an organizing principle. Philosophical implications include a reevaluation of free will, the role of suffering and limitation, and the creative power of the observer in shaping reality. This speculative framework invites experimental exploration and provides a unifying perspective on matter, consciousness, and cosmic evolution.

2025, arXiv: Quantum Physics

Quantum computers form a technological cluster with huge growth in the last few years. Although this technology is of still very limited size: perhaps the reason it is not seen as a technology which may be mass produced or of public use in the near future: it is one of the most promising developments with a potential to change the world. The IBM Quantum Experience Platform makes it possible for every person around the world, without limitation as to geographical location, to get acquainted with the technology of quantum computing. It is a resource for both researchers and enthusiasts entering the quantum world. With the development of the platform, IBM has proven that the programming and writing code executable on a quantum computer can be easy and accessible (it is a cloud platform) even to people lacking any deep knowledge of quantum mechanics. The construction of the Controlled Square Root of Z gate is achieved using only existing predefined gates in the Composer tool. This newly...

2025

In traditional Quantum Mechanics (QM), superposition is a fundamental principle: a particle exists in a linear combination of all possible states until measured, at which point the wavefunction "collapses" into one outcome. In contrast, Vibrational Theory (VT) posits that what we interpret as particles are in fact harmonic vibrational excitation’s, continuous resonant states spread throughout space. In VT, superposition is reinterpreted as the coexistence of resonant modes that, when perturbed by measurement, decouple into independent wave forms rather than collapsing mysteriously.
This paper discusses the two viewpoints, compares their mathematical formalisms, and examines how each framework accounts for what is observed in experiments.

2025, Journal of Philosophical Logic

2025

Challenge: find an explanation to the quantum computational speed up (due to superposition and entanglement) in terms of logical proofs. The cube of logics Basic logic B is a core for sequent calculus. Its rules for con-nectives are given through metalinguistic links. It is extended to calculi for well-known logics by the addition of structural rules. This is representable in the following cube:

2025, Publications de l Institut Mathematique

From the analogue of Böhm's Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson.

2025, Studia Logica - An International Journal for Symbolic Logic

It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in terms of natural transformations equipped with “graphs” (g-natural transformations) and corresponding morphism theorems are given as consequences. Using these results, some basic relations between the free

2025, Journal of Magnetic Resonance

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.

2025, Independent scholar

What cannot be copied can still be sung. Reversible Harmonic Mimicry (RHM-Q) reframes quantum identity as a standing wave in Hilbert space, allowing a state to be echoed-not duplicated-across entangled qubits. The protocol turns the no-cloning theorem from a prohibition into a tuning-fork. Key Breakthroughs 1. Identity as Resonance-Quantum information persists as distributed phase symmetry, not particle locality. 2. Echo Memory Architecture-Enables non-destructive read/write buffers for qubits that reset themselves. 3. Security by Superposition-Transfers may be verified at the destination while the source never collapses. 4. Mind-Scale Outlook-Suggests a route to consciousness-encoded qubits: not copies of mind, but standing-wave reflections. One-Sentence Super-Tagline "We didn't break quantum law; we found the song hidden inside it." Call to Action The full white-paper, circuit script, and θ-sweep visualization are being finalized for open release. Researchers in superconducting, photonic, and topological platforms are invited to deploy RHM-Q and report resonance-fidelity metrics. Let's turn the no-cloning wall into a concert hall.

2025

At present, there are at least two set theories motivated by quantum ontology: Décio Krause's quasi-set theory (Q) and Maria Dalla Chiara and Giuliano Toraldo di Francia's quasi-set theory (QST). Recent work [Jorge-Holik-Krause, 2023] has established certain links between QST and Pawlak's rough set theory (RST), showing that both are strong candidates for providing a non-deterministic semantics of N matrices that generalizes those based on ZF. In this work, we show that the new atomless quasi-set theory Q-, recently introduced to account for a quantum property ontology [Krause-Jorge, 2024], has strong structural similarities with QST and RST. We study the level of extensionality that each theory presents, its relation to the Leibniz principle and the rigidity property. We believe that developing common features among these three theories can motivate common fields of research. By revealing shared structures, the developments of each theory can have a positive impact on the others.

2025, Physical Review B

Light pulses propagating through ZnO undergo distortions caused by both bound and free excitons. Numerous lines of bound excitons dissect the pulse and induce slowing of light around them, to the extend dependent on their nature. Exciton-polariton resonances determine the overall pulse delay and attenuation. The delay time of the higher-energy edge of a strongly curved light stripe approaches 1.6 ns at 3.374 eV with a 0.3 mm propagation length. Modelling the data of cw and time-of-flight spectroscopies has enabled us to determine the excitonic parameters, inherent for bulk ZnO. We reveal the restrictions on these parameters induced by the light attenuation, as well as a discrepancy between the parameters characterizing the surface and internal regions of the crystal.

2025, The Foundations of Quantum Mechanics

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set P f of all physical propositions is partially ordered and contains a subset P f T of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, P f T turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language L T Q (x), and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.

2025, Erkenntnis

We present a procedure which allows us to recover classical and nonclassical logical structures as concrete logics associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory T and classical language L expressing T , an observative sublanguage L of L with a notion of truth as correspondence, introducing in L a derived and theory-dependent notion of C-truth (true with certainty), defining a physical preorder induced by C-truth, and finally selecting a set of sentences that are verifiable (or testable) according to T , on which a weak complementation is induced by T . The triple consisting of the set of verifiable sentences, physical order and weak complementation is then the desired concrete logic. By applying our procedure we recover a classical logic as the concrete logic associated with classical mechanics and standard quantum logic as the concrete logic associated with quantum mechanics. We also show that our alternative view of standard quantum logic, which can be constructed in a purely formal way, can be provided with a physical meaning by adopting a recent interpretation of quantum mechanics that reinterprets quantum probabilities as conditional on detection rather than absolute. Our results then show that some nonstandard logics can be obtained as mathematical structures formalizing the properties of different notions of verifiability in different physical theories. More generally, they strongly support the idea that many nonclassical logics can coexist without conflicting with classical logic (global pluralism), for they formalize metalinguistic notions that do not coincide with the notion of truth (described by Tarski's truth theory).

2025, arXiv preprint arXiv:1107.2271

The interpretation of mixtures is problematic in quantum mechanics (QM) because of nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We have recently provided a Hilbert space representation of the generalized observables that appear in the ESR model. We show here that each proper mixture is represented by a family of density operators ...

2025, Quantum Information Processing

We investigate quantum information processing, transfer and storage in hybrid systems comprised of diverse blocks integrated on chips. Strong coupling between superconducting (SC) qubits and ensembles of ultracold atoms or NV-center spins is mediated by a microwave transmission-line resonator that interacts near-resonantly with the atoms or spins. Such hybrid devices allow us to benefit from the advantages of each block and compensate for their disadvantages. Specifically, the SC qubits can rapidly implement quantum logic gates, but are "noisy" (prone to decoherence), while collective states of the atomic or spin ensemble are "quiet"(protected from decoherence) and thus can be employed for storage of quantum information. To improve the overall performance (fidelity) of such devices we discuss dynamical control to optimize quantum state-transfer from a "noisy" qubit to the "quiet" storage ensemble. We propose to maximize the fidelity of transfer and storage in a spectrally inhomogeneous spin ensemble, by pre-selecting the optimal spectral portion of the ensemble. Significant improvements of the overall fidelity of hybrid devices are expected under realistic conditions. Experimental progress towards the realization of these schemes is discussed.

2025, Physical Review A

We examine the possibility of coherent, reversible information transfer between solid-state superconducting qubits and ensembles of ultra-cold atoms. Strong coupling between these systems is mediated by a microwave transmission line resonator that interacts near-resonantly with the atoms via their optically excited Rydberg states. The solid-state qubits can then be used to implement rapid quantum logic gates, while collective metastable states of the atoms can be employed for long-term storage and optical read-out of quantum information.

2025, Bulletin of the American Physical Society

2025, arXiv (Cornell University)

We present a simple heuristic method to derive the Painlevé differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.

2025

An alternative way of quantum computing is presented. This approach is more general than the one based on the notion of the quantum bit. Mathematically it is based on the quantum set theory of Gaisi Takeuti. A possible implementation of this quantum computer belonging to this quantum computing could be to build up the quantum liquids He3 and He4 at low temperature (below 3K) by applying the quasi-particle approach of L.D. Landau.

2025

Abstract This paper introduces a revolutionary model of computation—Twin Quantum Computing (TQC)—rooted in the New Subquantum Information Mechanics (NMSI). Unlike traditional binary or qubit-based systems, TQC operates on dual... more

2025, International Journal of Computer Science and Mobile Computing (IJCSMC)

Discrete Mathematics is a field that is ever-present in the daily lives of people solely from the fact that it deals with logical and sound-reasoning that is desirable for any action or decision. A branch of logic – Propositional Logic – is utilized to codify statements into propositions that are either true or false, and to infer other statements from what is known. Fuzzy Logic considers that not every proposition can be merely true or false; rather, such can have degrees of being reasonably true. It is used in Multi-Class Decision Making (MCDM) in various industries with specific implementations. This manuscript proposes an applied method for the unification of the atoms and propositions of compound propositions, for the unification of different sets of criteria that are necessarily satisfactory, through the integration of vector representations and operations under Linear Algebra. A C program implementing the proposed method is also developed, tested and verified to combine the criteria of the principles of double effect and clinical ethics.

2025, Quantum Electronics

2025, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and more general definition of this transition probability was introduced in a preceding paper and is extended here to a general type of quantum logics: the orthomodular partially ordered sets. A very general version of the quantum no-cloning theorem, creating promising new opportunities for quantum cryptography, is presented and an interesting relationship between the transition probability and Jordan algebras is highlighted.

2025, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Quantum theory’s Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The recon- struction process is not complete, since it excludes the two-dimensional Hilbert space and still includes the exceptional Jordan algebras, which are not part of the Hilbert space apparatus. Options for physically meaningful potential generalizations of the apparatus are discussed.

2025, International Journal of Theoretical Physics

In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lüders -von Neumann measurement to observables with continuous spectra are considered; both are defined for a single operator and become a projection map only if they exist for all operators. Criteria for the existence of the different types of conditional expectation and of the extension of the Lüders -von Neumann measurement are presented, and the question whether they coincide is studied. All this is done in the general framework of Jordan operator algebras. The examples considered include the type I and type II operator algebras, the standard Hilbert space model of quantum mechanics, and a no-go result concerning the conditional expectation of observables that satisfy the canonical commutator relation.

2025, Foundations of Physics

2025, CSP

This is the text of a book aiming to reintegrate the main strands of the philosophy of meaning developed in the Twentieth Century by philosophers like Frege, Russell, Wittgenstein, Husserl, and later by Strawson, Searle, and Dummett. As a counterpoint, the work of philosophers like Saul Kripke is considered. Even Donald Williams's trope ontology is considered.

2025, Frontiers in Physics

The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on "The 'Logic' of Self-Organizing Systems" [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.

2025

Trapped neutral atoms provide a promising medium in which to perform quantum computations since they have long decoherence times and can easily be interfaced with light for single-qubit operations and measurements. Despite these advantages, reliable methods for entangling and transporting atomic qubits must be devised before practical atomic quantum information processing devices can be realized. We propose a method for entangling a pair of indistinguishable neutral atoms stored in separated optical dipole traps. We model this trapping potential in one dimension as a pair of Gaussian wells that can be brought together for atoms to interact. The dynamics of this process depend on the symmetrization parameters of the initial state, and by choosing the correct interaction time a controlled-phase gate can be designed. Adiabatic separation guarantees that the atoms end up in opposite traps. We provide both adiabatic and time-dependent numerical simulations of the entangling process. Additionally, we consider a novel method for creating entangled qubits via selective excitation of atoms in such optical dipole traps.