A generic approach to the quantum mechanical transition probability
arXiv:2110.12754 · doi:10.1098/rspa.2021.0821
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.
22 pages, correction in the proof of Proposition 4.3
References in corpus (6)
- Characterizing quantum theory in terms of information-theoretic constraints
- A generalized no-broadcasting theorem
- Cloning and Broadcasting in Generic Probabilistic Theories
- Non-Boolean probabilities and quantum measurement
- No-Cloning Theorem on Quantum Logics
- Imperfect cloning operations in algebraic quantum theory