131 citations · 799 across the 72 of their papers we have counts for
74 papers
Exponential arcs in manifolds of quantum states
Jan Naudts
The manifold under consideration consists of the faithful normal states on a sigma-finite von Neumann algebra in standard form. Tangent planes and approximate tangent planes are di…
Exponential arcs in the manifold of vector states on a sigma-finite von Neumann algebra
Jan Naudts
This paper introduces the notion of exponential arcs in Hilbert space and of exponential arcs connecting vector states on a sigma-finite von Neumann algebra in its standard represe…
Parameter-free description of the manifold of non-degenerate density matrices
Jan Naudts
The paper gives a definition of exponential arcs in the manifold of non-degenerate density matrices and uses it as a starting point to develop a parameter-free version of non-commu…
Gauge transformations of a relativistic field of quantum harmonic oscillators
Jan Naudts
A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the numbe…
Update of prior probabilities by minimal divergence
Jan Naudts
The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The optimal update is obtained by minimizing eithe…
Log-affine geodesics in the manifold of vector states on a von Neumann algebra
Jan Naudts
This paper introduces the notion of a log-affine geodesic connecting two vector states on a von Neumann algebra. The definition is linked to the standard notion of Boltzmann-Gibbs…