**Mladen Pavicic
**

Department of Mathematics, University of Zagreb, GF, Kaciceva 26, POB-217, HR-10001 Zagreb, Croatia; mpavicic@faust.irb.hr; http://m3k.grad.hr/pavicic

** Abstract. **
The following results obtained within
a project of finding algebra of states in a general purpose
quantum computer are reported: 1. all operations of an
orthomodular lattice, including the identity, are five-fold
defined; 2. there are non-orthomodular models for both
quantum and classical logics; 3. there is a 4-variable
orthoarguesian lattice condition which contains all known
orthoarguesian lattice conditions including 6- and 5-variable
ones.

**PACS numbers: ** 03.65.Bz, 02.10.By, 02.10.Gd

**Keywords: ** quantum logic, orthomodular
lattices, quantum computation, classical logic, Boolean
algebra, orthoarguesian properties, models.