Operator Deformations in Quantum Measurement Theory

Operator structures in quantum information theory

Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B(H). This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗algebras and W ∗algebras (with the latter also known as von Neumann algebras). In the 1970’s these were u...

On momentum operator in quantum field theory

The interrelations between the two definitions of momentum operator, via the canonical energy-momentum tensorial operator and as translation operator (on the operator space), are studied in quantum field theory. These definitions give rise to similar but, generally, different momentum operators, each of them having its own place in the theory. Some speculations on the relations between quantum ...

Operational Quantum Theory; Measurement Theory

Algebraic Quantum Field Theory and Operator Algebras

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as " why mathematicians are/should be interested in algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...

The operator tensor formulation of quantum theory.

In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An o...