TY  - JOUR
AU  - Aldana, M.
AU  - Lledo, M. A.
PY  - 2023
DA  - 2023//
TI  - The Fuzzy Bit
T2  - Symmetry-Basel
JO  - Symmetry-Basel
SP  - 2103
EP  - 25pp
VL  - 15
IS  - 12
PB  - Mdpi
KW  - fuzzy sets
KW  - quantum logic
KW  - multivalued logic
KW  - Quantum Mechanics
AB  - 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.
UR  - https://arxiv.org/abs/2311.14083
UR  - https://doi.org/10.3390/sym15122103
DO  - 10.3390/sym15122103
LA  - English
N1  - WOS:001131238400001
ID  - Aldana+Lledo2023
ER  -