Quantum transition probability in convex sets and self-dual cones
- URL: http://arxiv.org/abs/2312.13213v1
- Date: Wed, 20 Dec 2023 17:28:47 GMT
- Title: Quantum transition probability in convex sets and self-dual cones
- Authors: Gerd Niestegge
- Abstract summary: We present a more elementary approach with a more generic structure for the observables.
The binary case gives rise to the generalized qubit models.
A novel geometric property that makes any compact convex set a matching state space is presented.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The interplay between the algebraic structure (operator algebras) for the
quantum observables and the convex structure of the state space has been
explored for a long time and most advanced results are due to Alfsen and
Shultz. Here we present a more elementary approach with a more generic
structure for the observables, which focuses on the transition probability of
the quantum logical atoms. The binary case gives rise to the generalized qubit
models and was fully developed in a preceding paper. Here we consider any case
with finite information capacity (binary means that the information capacity is
2). A novel geometric property that makes any compact convex set a matching
state space is presented. Generally, the transition probability is not
symmetric; if it is symmetric, we get an inner product and a self-dual cone.
The emerging mathematical structure comes close to the Euclidean Jordan
algebras and becomes a new mathematical model for a potential extension of
quantum theory.
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