Kochen-Specker Algorithms for Qunits

Algorithms for finding arbitrary sets of Kochen-Specker (KS) qunits (n-level systems) as well as all the remaining vectors in a space of an arbitrary dimension are presented. The algorithms are based on linear MMP diagrams which generate orthogonalities of KS qunits, on an algebraic definition of states on the diagrams, and on nonlinear equations corresponding to MMP diagrams whose solutions are either KS qunits or the remaining vectors of a chosen space depending on whether the diagrams allow 0-1 states or not. The complexity of the algorithms is polynomial. New results obtained with the help of the algorithms are presented.Comment: 4 pages, 4 figures, appeared in Barnett, S.M., Andersson, E., Jeffers, J., Ohberg, P., and Hirota, O., (Eds), QCMC 2004. Quantum Communication, Measurement and Computing: The Seventh International Conference on Quantum Communication, Measurement and Computing held in Glasgow, United Kingdom, 25-29 July 2004, American Institute of Physics Conference Proceedings 734, 2004, pp. 195-198, under the title "Kochen-Specker algorithms for qubits"; qubits changed into qunits here; 3 typos corrected; Web page: http://m3k.grad.hr/pavici

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