The Fuzzy Bit-Reference-Cited by-同舟云学术

The Fuzzy Bit

Published:2023-11-23 Issue:12 Volume:15 Page:2103
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Aldana Milagrosa¹,Lledó María Antonia²^ORCID

Affiliation:

1. Departamento de Ciencias de la Tierra, Universidad Simón Bolívar, Valle de Sartenejas, Baruta 89000, Venezuela

2. Departament de Física Teòrica, Universitat de València and IFIC (CSIC-UVEG) C/Dr. Moliner, 50, 46100 Burjassot, Spain

Abstract

In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, which establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families of fuzzy sets, is applied to the Birkhoff–von Neumann logic, the lattice of projectors of a Hilbert space. Three cases are considered: the qubit, two qubits entangled, and a qutrit ‘nested’ inside the two entangled qubits. The membership functions of the fuzzy sets are explicitly computed and all the connectives of the fuzzy sets are interpreted as operations with these particular membership functions. In this way, a complete picture of the standard quantum logic in terms of fuzzy sets is obtained for the systems considered.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/12/2103/pdf

Reference23 articles.

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4. Łukasiewicz, J. (1913). Logical Foundations of Probability Theory, Akademien der Wissenschaften Schweiz.

5. Fuzzy sets;Zadeh;Inf. Control,1965