25 citations · 144 across the 25 of their papers we have counts for
25 papers
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…
Non-symmetric transition probability in generalized qubit models
Gerd Niestegge
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced i…
A generic approach to the quantum mechanical transition probability
Gerd Niestegge
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 repre…
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…
Quantum key distribution without the wavefunction
Gerd Niestegge
A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communicati…
Quantum teleportation and Grover's algorithm without the wavefunction
Gerd Niestegge
In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm ar…
Non-classical conditional probability and the quantum no-cloning theorem
Gerd Niestegge
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though s…
A Generalized Quantum Theory
Gerd Niestegge
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed sta…
Dynamical Correspondence in a Generalized Quantum Theory
Gerd Niestegge
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general cla…
Super quantum probabilities and three-slit experiments -- Wright's pentagon state and the Popescu-Rohrlich box require third-order interference
Gerd Niestegge
Quantum probabilities differ from classical ones in many ways, e.g., by violating the well-known Bell and CHSH inequalities or another simple inequality due to R. Wright. The latte…
Three-slit experiments and quantum nonlocality
Gerd Niestegge
An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson's bound for the no…
Third-order interference and a principle of `quantumness'
Gerd Niestegge
Are there physical, probabilistic or information-theoretic principles which characterize the quantum probabilities and distinguish them from the classical case as well as from othe…
Physical Reality and Information - Three Hypotheses
Gerd Niestegge
Since its emergence, quantum mechanics has been a challenge for an understanding of reality which is based on our intuition in a classical world. Nevertheless, it has often been tr…
A Representation of Quantum Measurement in Nonassociative Algebras
Gerd Niestegge
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event s…
Different Types of Conditional Expectation and the Lueders - von Neumann Quantum Measurement
Gerd Niestegge
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an e…
Conditional expectations associated with quantum states
Gerd Niestegge
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is prese…
Why Do the Quantum Observables Form a Jordan Operator Algebra?
Gerd Niestegge
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts…
Non-Boolean probabilities and quantum measurement
Gerd Niestegge
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and mo…
A Representation of Quantum Measurement in Order-Unit Spaces
Gerd Niestegge
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability…
A hierarchy of compatibility and comeasurability levels in quantum logics with unique conditional probabilities
Gerd Niestegge
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated…