Notes on conditional states and symmetric dierences
Oľga Nánásiová, Ahmad Tarmizi Mohammed · 2006
The theory of orthomodular lattice and its relationships that depend on s-map and condi-tional states definitions has shown in several types of probabilistic relations. An orthomodularlattice with a conditional states can be applied and defined as a model for non-compatible events.Studying of s-maps or conditional states on an orthomodular lattice helps us to describe suchproperties of random events, which are difficult to be described by Boolean algebra. In a par-ticularly observed quantum or classical system the information, that we cannot access results inour description of the system be coming mixed even if we have perfect initial knowledge.That is, if the system is quantum the conditional states will be given by a state matrix and ifclassical, the conditional states will be given by a probability distribution. We show conditionswhen a quantum system has the same properties as the classical probability space.Acknowledgement. This work was supported by Science and Technology Assistance AgencyunderthecontractNo. APVT-20-003204, VEGA-1/3014/06, VEGA-1/3321/06, VEGA-1/3006/06