Results for 'Qubit'

47 found
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  1.  36
    Qubit Cosmology.Haikel Mubarek - manuscript
    Understanding the fabric and mechanism of the universe as an information processing procedure is one way of approaching the mystery of reality. And there should be ingredients of information for such a description. But if we are going to start from the origin of the universe, those ingredients should be found at the beginning. What is assumed, in this paper, to be found at the beginning of the universe is an outward-inward vanishing of a point. And those are taken to (...)
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  2.  54
    Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental Time.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (22):1-24.
    Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be (...)
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  3. What is The Reason to Use Clifford Algebra in Quantum Cognition? Part I: “It From Qubit” On The Possibility That the Amino Acids Can Discern Between Two Quantum Spin States.Elio Conte - 2012 - Neuroquantology 10 (3):561-565.
    Starting with 1985, we discovered the possible existence of electrons with net helicity in biomolecules as amino acids and their possibility to discern between the two quantum spin states. It is well known that the question of a possible fundamental role of quantum mechanics in biological matter constitutes still a long debate. In the last ten years we have given a rather complete quantum mechanical elaboration entirely based on Clifford algebra whose basic entities are isomorphic to the well known spin (...)
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  4.  56
    Quantity in Quantum Mechanics and the Quantity of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (47):1-10.
    The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case of “unitary” qubits. (...)
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  5.  74
    Matter as Information. Quantum Information as Matter.Vasil Penchev - 2016 - Nodi. Collana di Storia Della Filosofia 2016 (2):127-138.
    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 (...)
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  6.  66
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7):1-57.
    In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...)
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  7.  71
    The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: The Physical, Mathematical and Philosophical Interpretations.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (3):1-22.
    A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can (...)
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  8. Natural Cybernetics of Time, or About the Half of Any Whole.Vasil Penchev - 2021 - Information Systems eJournal (Elsevier: SSRN) 4 (28):1-55.
    Norbert Wiener’s idea of “cybernetics” is linked to temporality as in a physical as in a philosophical sense. “Time orders” can be the slogan of that natural cybernetics of time: time orders by itself in its “screen” in virtue of being a well-ordering valid until the present moment and dividing any totality into two parts: the well-ordered of the past and the yet unordered of the future therefore sharing the common boundary of the present between them when the ordering is (...)
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  9. Atomism in Quantum Mechanics and Information.Vasil Penchev - 2020 - Metaphysics eJournal (Elsevier: SSRN) 13 (12):1-11.
    The original conception of atomism suggests “atoms”, which cannot be divided more into composing parts. However, the name “atom” in physics is reserved for entities, which can be divided into electrons, protons, neutrons and other “elementary particles”, some of which are in turn compounded by other, “more elementary” ones. Instead of this, quantum mechanics is grounded on the actually indivisible quanta of action limited by the fundamental Planck constant. It resolves the problem of how both discrete and continuous (even smooth) (...)
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  10. A Quantum Computer in a 'Chinese Room'.Vasil Penchev - 2020 - Mechanical Engineering eJournal (Elsevier: SSRN) 3 (155):1-8.
    Pattern recognition is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary patterns in any data. That ability of universal pattern recognition is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain quite (...)
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  11. The Quantity of Quantum Information and Its Metaphysics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (18):1-6.
    The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time (...)
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  12. Natural Argument by a Quantum Computer.Vasil Penchev - 2020 - Computing Methodology eJournal (Elsevier: SSRN) 3 (30):1-8.
    Natural argument is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary natural arguments in any data. That ability of natural argument is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain quite (...)
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  13. The Isomorphism of Minkowski Space and the Separable Complex Hilbert Space and its Physical Interpretation.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier:SSRN) 13 (31):1-3.
    An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the (...)
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  14. What Is Quantum Information? Information Symmetry and Mechanical Motion.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-7.
    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 (...)
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  15. Main Concepts in Philosophy of Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (31):1-4.
    Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present as a choice among infinitely many alternatives, (...)
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  16.  88
    The Kochen - Specker Theorem in Quantum Mechanics: A Philosophical Comment (Part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine (...)
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  17.  72
    God's Dice.Vasil Penchev - 2015 - In S. Oms, J. Martínez, M. García-Carpintero & J. Díez (eds.), Actas: VIII Conference of the Spanish Society for Logic, Methodology, and Philosophy of Sciences. Barcelona: Universitat de Barcelona. pp. 297-303.
    Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be (...)
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  18.  65
    Is Mass at Rest One and the Same? A Philosophical Comment: On the Quantum Information Theory of Mass in General Relativity and the Standard Model.Vasil Penchev - 2014 - Journal of SibFU. Humanities and Social Sciences 7 (4):704-720.
    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 (...)
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  19.  53
    Quantum Information as the Information of Infinite Collections or Series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time (...)
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  20. Отвъд машината на Тюринг: квантовият компютър.Vasil Penchev - 2014 - Sofia: BAS: ISSK (IPS).
    Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum computer (...)
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  21. On the (Im)Possibility of Scalable Quantum Computing.Andrew Knight - manuscript
    The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation as irreversible (...)
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  22.  44
    The Symmetries of Quantum and Classical Information. The Ressurrected “Ether" of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (41):1-36.
    The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...)
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  23. Fermat’s Last Theorem Proved in Hilbert Arithmetic. III. The Quantum-Information Unification of Fermat’s Last Theorem and Gleason’s Theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...)
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  24.  38
    Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal 14 (14):1-37.
    Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism (...)
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  25.  54
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. II. Its Proof in Hilbert Arithmetic by the Kochen-Specker Theorem with or Without Induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum (...)
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  26. The Identity of Logic and the World in Terms of Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (21):1-4.
    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 (...)
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  27.  66
    Quantum Phenomenology as a “Rigorous Science”: The Triad of Epoché and the Symmetries of Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (48):1-18.
    Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...)
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  28. Negative and Complex Probability in Quantum Information.Vasil Penchev - 2012 - Philosophical Alternatives 21 (1):63-77.
    “Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in quantum correlations … and for wave-particle (...)
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  29.  53
    “Two Bits Less” After Quantum-Information Conservation and Their Interpretation as “Distinguishability / Indistinguishability” and “Classical / Quantum”.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (46):1-7.
    The paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly “distinguishability / indistinguishability” and “classical / quantum”, available implicitly in the concept of quantum indistinguishability can be interpreted as two “missing” bits of classical information, which are to be added after teleportation of quantum information to be restored the initial state unambiguously. That new understanding of quantum indistinguishability is linked to the (...)
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  30. Free Will in Human Behavior and Physics.Vasil Penchev - 2020 - Labor and Social Relations 30 (6):185-196.
    If the concept of “free will” is reduced to that of “choice” all physical world shares the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, (...)
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  31. The Frontier of Time: The Concept of Quantum Information.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (17):1-5.
    The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number of (...)
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  32. God, Logic, and Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-10.
    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 (...)
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  33. General Relativity and Quantum Gravity in Terms of Quantum Measure: A Philosophical Comment.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (17):1-37.
    The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a (...)
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  34. Choice, Infinity, and Negation: Both Set-Theory and Quantum-Information Viewpoints to Negation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (14):1-3.
    The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds to set-theory (...)
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  35.  79
    Problem of the Direct Quantum-Information Transformation of Chemical Substance.Vasil Penchev - 2020 - Computational and Theoretical Chemistry eJournal (Elsevier: SSRN) 3 (26):1-15.
    Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...)
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  36. What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22):1-32.
    Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...)
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  37.  47
    Quantum Measure From a Philosophical Viewpoint.Vasil Penchev - 2014 - Journal of Siberian Federal University. Humanities and Social Sciences 7 (1):4-19.
    The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a (...)
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  38.  49
    Квантовият компютър: квантовите ординали и типовете алгоритмична неразрешимост.Vasil Penchev - 2005 - Philosophical Alternatives 14 (6):59-71.
    A definition of quantum computer is supposed: as a countable set of Turing machines on the ground of: quantum parallelism, reversibility, entanglement. Qubit is the set of all the i–th binary location cells transforming in parallel by unitary matrices. The Church thesis is suggested in the form relevat to quantum computer. The notion of the non–finite (but not infinite) potency of a set is introduced .
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  39. Schroedinger's Register: Foundational Issues and Physical Realization.Stephen Pink & Stanley Martens - manuscript
    This work-in-progress paper consists of four points which relate to the foundations and physical realization of quantum computing. The first point is that the qubit cannot be taken as the basic unit for quantum computing, because not every superposition of bit-strings of length n can be factored into a string of n-qubits. The second point is that the “No-cloning” theorem does not apply to the copying of one quantum register into another register, because the mathematical representation of this copying (...)
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  40. The 'Noncausal Causality' of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (45):1-7.
    The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by (...)
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  41.  61
    Hilbert Arithmetic as a Pythagorean Arithmetic: Arithmetic as Transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
    The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...)
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  42. A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory.Vasil Penchev - 2020 - Information Theory and Research eJournal 1 (15):1-13.
    A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section I. (...)
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  43. Two Strategies to Infinity: Completeness and Incompleteness. The Completeness of Quantum Mechanics.Vasil Penchev - 2020 - High Performance Computing eJournal 12 (11):1-8.
    Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...)
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  44. Universal Logic in Terms of Quantum Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (9):1-5.
    Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space can be interpreted. The (...)
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  45. Cognition According to Quantum Information: Three Epistemological Puzzles Solved.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (20):1-15.
    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 (...)
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  46.  59
    The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite sets. (...)
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  47.  53
    A New Reading and Comparative Interpretation of Gödel’s Completeness (1930) and Incompleteness (1931) Theorems.Vasil Penchev - 2016 - Логико-Философские Штудии 13 (2):187-188.
    Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most (...)
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