A generic approach to the quantum mechanical transition probability

• URL: http://arxiv.org/abs/2110.12754v2
• Date: Wed, 13 Apr 2022 12:48:19 GMT
• Title: A generic approach to the quantum mechanical transition probability
• Authors: Gerd Niestegge
• Abstract summary: In quantum theory, the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A very general version of the quantum no-cloning theorem, creating promising new opportunities for quantum cryptography is presented.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and more general definition of this transition probability was introduced in a preceding paper and is extended here to a general type of quantum logics: the orthomodular partially ordered sets. A very general version of the quantum no-cloning theorem, creating promising new opportunities for quantum cryptography, is presented and an interesting relationship between the transition probability and Jordan algebras is highlighted.

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