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In quantum theory, the modulus-square of the inner product of two normalizedHilbert space elements is to be interpreted as the transition probabilitybetween the pure states represented by these elements. A probabilisticallymotivated and more general definition of this transition probability wasintroduced in a preceding paper and is extended here to a general type ofquantum logics: the orthomodular partially ordered sets. A very general versionof the quantum no-cloning theorem, creating promising new opportunities forquantum cryptography, is presented and an interesting relationship between thetransition probability and Jordan algebras is highlighted.

A generic approach to the quantum mechanical transition probability