# Introduction to quantum probability

 Title: Introduction to quantum probability Description: This thesis is a review of the quantum logic approach to quantum probability theory which was first studied by Birkhoff and von Neumann in 1936 . Our study is based on the more general quantum structure which is known as the $\sigma$ -orthocomplete orthomodular poset or quantum logic . We introduce the definitions of states and observables and show that the quantum probability theory is a generalization of the classical probability theory due to Kolmogorov . Discussions about joint distributions of observables are given , and we also give the general expression of the uncertainty relation in the logico -algebraic sense which generalizes the well -known Heisenberg uncertainty relation . Two examples , the classical probability structure of Kolmogorov and the Hilbert space quantum logic , are given as illustrations throughout the whole discussion . URI: http : / /hdl .handle .net /2346 /ETD -TTU -2011 -08 -1723 Date: 2012-11-29

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