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On the homogeneity of the quantum transition probability
Gerd Niestegge
In the years 1952 and 1965, H.-C. Wang and U. Hirzebruch showed that the two-point homogeneous compact spaces with convex metrics are isometric to the spheres, the real, complex, o…
Bit symmetry entails the symmetry of the quantum transition probability
Gerd Niestegge
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understandi…
Quantum transition probability in convex sets and self-dual cones
Gerd Niestegge
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…
Quantum Probability's Algebraic Origin
Gerd Niestegge
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have ver…
Local tomography and the role of the complex numbers in quantum mechanics
Gerd Niestegge
Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a…
A simple and quantum-mechanically motivated characterization of the formally real Jordan algebras
Gerd Niestegge
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logi…