Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (7)

Search Parameters:
Keywords = operational quantum axiomatics

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
84 pages, 6996 KiB  
Article
The Philosophy of Nature of the Natural Realism. The Operator Algebra from Physics to Logic
by Gianfranco Basti
Philosophies 2022, 7(6), 121; https://doi.org/10.3390/philosophies7060121 - 26 Oct 2022
Cited by 2 | Viewed by 5029
Abstract
This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern [...] Read more.
This contribution is an essay of formal philosophy—and more specifically of formal ontology and formal epistemology—applied, respectively, to the philosophy of nature and to the philosophy of sciences, interpreted the former as the ontology and the latter as the epistemology of the modern mathematical, natural, and artificial sciences, the theoretical computer science included. I present the formal philosophy in the framework of the category theory (CT) as an axiomatic metalanguage—in many senses “wider” than set theory (ST)—of mathematics and logic, both of the “extensional” logics of the pure and applied mathematical sciences (=mathematical logic), and the “intensional” modal logics of the philosophical disciplines (=philosophical logic). It is particularly significant in this categorical framework the possibility of extending the operator algebra formalism from (quantum and classical) physics to logic, via the so-called “Boolean algebras with operators” (BAOs), with this extension being the core of our formal ontology. In this context, I discuss the relevance of the algebraic Hopf coproduct and colimit operations, and then of the category of coalgebras in the computations over lattices of quantum numbers in the quantum field theory (QFT), interpreted as the fundamental physics. This coalgebraic formalism is particularly relevant for modeling the notion of the “quantum vacuum foliation” in QFT of dissipative systems, as a foundation of the notion of “complexity” in physics, and “memory” in biological and neural systems, using the powerful “colimit” operators. Finally, I suggest that in the CT logic, the relational semantics of BAOs, applied to the modal coalgebraic relational logic of the “possible worlds” in Kripke’s model theory, is the proper logic of the formal ontology and epistemology of the natural realism, as a formalized philosophy of nature and sciences. Full article
(This article belongs to the Special Issue Contemporary Natural Philosophy and Philosophies - Part 3)
Show Figures

Figure 1

27 pages, 1656 KiB  
Article
Human Perception as a Phenomenon of Quantization
by Diederik Aerts and Jonito Aerts Arguëlles
Entropy 2022, 24(9), 1207; https://doi.org/10.3390/e24091207 - 29 Aug 2022
Cited by 14 | Viewed by 4005
Abstract
For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of ‘categorical perception’ has put us on track to find a possible [...] Read more.
For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of ‘categorical perception’ has put us on track to find a possible deeper cause of the presence of this quantum structure in human cognition. Thus, we show that in an archetype of human perception consisting of the reconciliation of a bottom up stimulus with a top down cognitive expectation pattern, there arises the typical warping of categorical perception, where groups of stimuli clump together to form quanta, which move away from each other and lead to a discretization of a dimension. The individual concepts, which are these quanta, can be modeled by a quantum prototype theory with the square of the absolute value of a corresponding Schrödinger wave function as the fuzzy prototype structure, and the superposition of two such wave functions accounts for the interference pattern that occurs when these concepts are combined. Using a simple quantum measurement model, we analyze this archetype of human perception, provide an overview of the experimental evidence base for categorical perception with the phenomenon of warping leading to quantization, and illustrate our analyses with two examples worked out in detail. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
Show Figures

Figure 1

8 pages, 280 KiB  
Article
Quantum Epistemology and Falsification
by Giacomo Mauro D’Ariano
Entropy 2022, 24(4), 434; https://doi.org/10.3390/e24040434 - 22 Mar 2022
Cited by 4 | Viewed by 2363
Abstract
The operational axiomatization of quantum theory in previous works can be regarded as a set of six epistemological rules for falsifying propositions of the theory. In particular, the Purification postulate—the only one that is not shared with classical theory—allows falsification of random-sequences generators, [...] Read more.
The operational axiomatization of quantum theory in previous works can be regarded as a set of six epistemological rules for falsifying propositions of the theory. In particular, the Purification postulate—the only one that is not shared with classical theory—allows falsification of random-sequences generators, a task classically unfeasible. Full article
(This article belongs to the Special Issue The Philosophy of Quantum Physics)
34 pages, 671 KiB  
Article
A Novel Approach to the Partial Information Decomposition
by Artemy Kolchinsky
Entropy 2022, 24(3), 403; https://doi.org/10.3390/e24030403 - 13 Mar 2022
Cited by 44 | Viewed by 9030
Abstract
We consider the “partial information decomposition” (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we [...] Read more.
We consider the “partial information decomposition” (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for constructing a multivariate PID. Our framework is defined in terms of a formal analogy with intersection and union from set theory, along with an ordering relation which specifies when one information source is more informative than another. Our definitions are algebraically and axiomatically motivated, and can be generalized to domains beyond Shannon information theory (such as algorithmic information theory and quantum information theory). In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation. We demonstrate our approach on numerous examples and show that it overcomes many drawbacks associated with previous proposals. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
Show Figures

Figure 1

43 pages, 499 KiB  
Article
Currencies in Resource Theories
by Lea Kraemer and Lídia del Rio
Entropy 2021, 23(6), 755; https://doi.org/10.3390/e23060755 - 15 Jun 2021
Cited by 3 | Viewed by 2803
Abstract
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. [...] Read more.
How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
23 pages, 1170 KiB  
Article
Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability
by Jan Walleczek
Entropy 2019, 21(1), 4; https://doi.org/10.3390/e21010004 - 21 Dec 2018
Cited by 4 | Viewed by 8453
Abstract
The inaccessibility to the experimenter agent of the complete quantum state is well-known. However, decisive answers are still missing for the following question: What underpins and governs the physics of agent inaccessibility? Specifically, how does nature prevent the agent from accessing, predicting, and [...] Read more.
The inaccessibility to the experimenter agent of the complete quantum state is well-known. However, decisive answers are still missing for the following question: What underpins and governs the physics of agent inaccessibility? Specifically, how does nature prevent the agent from accessing, predicting, and controlling, individual quantum measurement outcomes? The orthodox interpretation of quantum mechanics employs the metaphysical assumption of indeterminism—‘intrinsic randomness’—as an axiomatic, in-principle limit on agent–quantum access. By contrast, ontological and deterministic interpretations of quantum mechanics typically adopt an operational, in-practice limit on agent access and knowledge—‘effective ignorance’. The present work considers a third option—‘objective ignorance’: an in-principle limit for ontological quantum mechanics based upon self-referential dynamics, including undecidable dynamics and dynamical chaos, employing uncomputability as a formal limit. Given a typical quantum random sequence, no formal proof is available for the truth of quantum indeterminism, whereas a formal proof for the uncomputability of the quantum random sequence—as a fundamental limit on agent access ensuring objective unpredictability—is a plausible option. This forms the basis of the present proposal for an agent-inaccessibility principle in quantum mechanics. Full article
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
Show Figures

Figure 1

31 pages, 651 KiB  
Article
Axiomatic Information Thermodynamics
by Austin Hulse, Benjamin Schumacher and Michael D. Westmoreland
Entropy 2018, 20(4), 237; https://doi.org/10.3390/e20040237 - 29 Mar 2018
Cited by 5 | Viewed by 5753
Abstract
We present an axiomatic framework for thermodynamics that incorporates information as a fundamental concept. The axioms describe both ordinary thermodynamic processes and those in which information is acquired, used and erased, as in the operation of Maxwell’s demon. This system, similar to previous [...] Read more.
We present an axiomatic framework for thermodynamics that incorporates information as a fundamental concept. The axioms describe both ordinary thermodynamic processes and those in which information is acquired, used and erased, as in the operation of Maxwell’s demon. This system, similar to previous axiomatic systems for thermodynamics, supports the construction of conserved quantities and an entropy function governing state changes. Here, however, the entropy exhibits both information and thermodynamic aspects. Although our axioms are not based upon probabilistic concepts, a natural and highly useful concept of probability emerges from the entropy function itself. Our abstract system has many models, including both classical and quantum examples. Full article
Show Figures

Figure 1

Back to TopTop