scholarly journals The Quantity of Quantum Information and Its Metaphysics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Infinite Series ◽  
Mathematical Structure ◽  
Axiom Of Choice ◽  
Classical Information ◽  
The Axiom Of Choice

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 after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question. Number and being (by the meditation of time), the natural and artificial turn out to be not more than different hypostases of a single common essence. This implies some kind of neo-Pythagorean ontology making related mathematics, physics, and technics immediately, by an explicit mathematical structure.

scholarly journals Quantum information as the information of infinite series

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Infinite Series ◽  
Axiom Of Choice ◽  
Classical Information ◽  
The Axiom Of Choice

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 after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question.1

scholarly journals Quantum information as the information of infinite collections or series

2021 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Infinite Series ◽  
Ordinal Number ◽  
Foundations Of Mathematics ◽  
Natural Numbers ◽  
Classical Information ◽  
Ordinal Numbers ◽  
The Axiom Of Choice

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 after measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics.

scholarly journals Cognition according to Quantum information: Three Epistemological Puzzles Solved

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Coherent State ◽  
Space Time ◽  
Axiom Of Choice ◽  
Statistical Ensemble ◽  
Quantum Processes ◽  
Quantum Leap ◽  
Before And After ◽  
The Axiom Of Choice

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 invariance and the nonlocality 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 invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity.The nonlocality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum invariance.Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics.,

scholarly journals Time: From the Totality to Quantum Information

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

The paper justifies the following theses: The totality can found time if the latter isaxiomatically represented by its “arrow” as a well-ordering. Time can found choice and thusinformation in turn. Quantum information and its units, the quantum bits, can be interpreted astheir generalization as to infinity and underlying the physical world as well as theultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.

scholarly journals Time and information in the foundations of physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
Foundations Of Physics ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

The paper justifies the following theses: The totality can found time if the latteris axiomatically represented by its “arrow” as a well-ordering. Time can found choice andthus information in turn. Quantum information and its units, the quantum bits, can beinterpreted as their generalization as to infinity and underlying the physical world as wellas the ultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.

scholarly journals Quantum Invariance

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Information ◽  
Coherent State ◽  
Set Theory ◽  
Ordered Set ◽  
Axiom Of Choice ◽  
Statistical Ensemble ◽  
Planck Constant ◽  
Physical Processes ◽  
Statistical Representation ◽  
The Axiom Of Choice

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. 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.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to a well-ordered set after measurement and thus requires the axiom of choice.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information.Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity.

scholarly journals The Frontier of Time: The Concept of Quantum Information

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Natural Number ◽  
Set Theory ◽  
Peano Arithmetic ◽  
Axiom Of Choice ◽  
The Axiom Of Choice ◽  
Infinite Set ◽  
In Virtue Of

A 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 elementary choices to be defined. This is the quantity of information defined both transcendentally and formally and thus, philosophically and mathematically. If one defines information specifically, as an elementary choice between finiteness (or mathematically, as any natural number of Peano arithmetic) and infinity (i.e. an actually infinite set in the meaning of set theory), the quantity of quantum information is defined. One can demonstrate that the so-defined quantum information and quantum information standardly defined by quantum mechanics are equivalent to each other. The equivalence of the axiom of choice and the well-ordering “theorem” is involved. It can be justified transcendentally as well, in virtue of transcendental equivalence implied by the totality. Thus, all can be considered as temporal as far anything possesses such a temporal counterpart necessarily. Formally defined, the frontier of time is the current choice now, a bit of information, furthermore interpretable as a qubit of quantum information.

scholarly journals The isomorphism of Minkowski space and the separable complex Hilbert space and its physical interpretation

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Special Relativity ◽  
Minkowski Space ◽  
Reference Frame ◽  
Physical Interpretation ◽  
Complex Hilbert Space ◽  
Axiom Of Choice ◽  
The Axiom Of Choice

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 invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”.

Quantum theory from quantum information: the purification route

2013 ◽  
Vol 91 (6) ◽  
pp. 475-478 ◽  
Author(s):  
Giulio Chiribella ◽  
Xiao Yuan
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Theory ◽  
Quantum Information ◽  
Foundations Of Quantum Mechanics ◽  
Mathematical Structure ◽  
Mathematical Language ◽  
Standard Quantum ◽  
Information Theoretic

Quantum information provided a new angle on the foundations of quantum mechanics, where the emphasis is placed on operational tasks pertaining to information-processing and computation. In this spirit, several authors have proposed that the mathematical structure of quantum theory could (and should) be rebuilt from purely information-theoretic principles. Here we review the particular route proposed by D'Ariano, Perinotti, and one of the authors (Chiribella et al. Phys. Rev. A, 84, 012311 (2011)), with the purpose of giving a synopsis of the informational principles therein, along with a translation of those principles into the mathematical language of standard quantum theory.

scholarly journals Quantum mechanics teaching resources from the Institute of Physics

2014 ◽  
pp. 40-43
Author(s):  
Antje Kohnle ◽  
Derek Raine
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Teaching And Learning ◽  
Hidden Variables ◽  
Mathematical Structure ◽  
Teaching Resources ◽  
Creative Commons ◽  
Introductory Course ◽  
Interpretations Of Quantum Mechanics ◽  
Two Level Systems

In December 2013, the Institute of Physics (IOP) launched a set of freely available resources at quantumphysics.iop.org for the teaching and learning of quantum mechanics. The website includes about 80 short articles written by experts in the field and 17 interactive simulations with accompanying activities for an introductory course in quantum mechanics starting from two-level systems. The articles are arranged according to five themes, including a focus on quantum information, interpretations of quantum mechanics, the mathematical structure of the theory, physics applications and historical experiments. The resources make topics such as entanglement, hidden variables and quantum information theory accessible to introductory-level students. They can be used flexibly for a variety of instructional aims at both the introductory and more advanced level. The website includes links to pre-readings, suggestions for further reading, a glossary of technical terms and allows users to rate their understanding of articles.Sharing of these resources is encouraged, with all usage under the Creative Commons CC BY-NC-ND licence. Solutions to problems and activities are available for instructors by emailing [email protected]. Instructors interested in evaluating these resources with their students in order to help us further develop and optimize the site are requested to contact the corresponding author.

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