195 research outputs found
Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices
It is shown that operations of equivalence cannot serve for building algebras
which would induce orthomodular lattices as the operations of implication can.
Several properties of equivalence operations have been investigated.
Distributivity of equivalence terms and several other 3 variable expressions
involving equivalence terms have been proved to hold in any orthomodular
lattice. Symmetric differences have been shown to reduce to complements of
equivalence terms. Some congruence relations related to equivalence operations
and symmetric differences have been considered.Comment: 13 pages, 1 figure, 1 table; To be published in International Journal
of Theoretical Physics, Vol. 42, No. 12 (2003); Web page:
http://m3k.grad.hr/pavici
Vector Generation of Contextual Sets
As quantum contextuality proves to be a necessary resource for universal
quantum computation, we present a general method for vector generation of
Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method
supersedes all three previous methods: (i) fortuitous discoveries of smallest
KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random
downward generation of sets from fortuitously obtained big master sets. In
contrast to previous works, we can generate master sets which contain all
possible KS sets starting with nothing but a few simple vector components. From
them we can readily generate all KS sets obtained in the last half a century
and any specified new KS sets. Herewith we can generate sufficiently large sets
as well as sets with definite required features and structures to enable
varieties of different implementations in quantum computation and
communication.Comment: 6 pages, 6 figures; Orally presented by M. Pavicic at Quantum
Technology International Conference 2018 (QTech 2018), Paris, France,
September 5-7, 2018; Extended version:
https://www.youtube.com/watch?v=Bw2vItz5tr
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