Formalization of Bohr's contextuality within theory of open quantum systems

TL;DR

This paper formalizes Bohr's original concept of quantum measurement contextuality within the framework of open quantum systems and quantum instruments, connecting foundational ideas to modern quantum information theory.

Contribution

It provides a mathematical formalization of Bohr's contextuality using the theory of open quantum systems and quantum instruments, bridging historical interpretation with contemporary quantum theory.

Findings

Formalization of Bohr's contextuality within open quantum systems

Application of the scheme of indirect measurements to contextuality

Connection of Bohr's ideas to quantum information theory

Abstract

In quantum physics, the notion of contextuality has a variety of interpretations which are typically associated with the names of their inventors, say Bohr, Bell, Kochen and Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for contextuality of quantum measurements rose again only in connection with the Bell inequality. The original Bohr's contextuality, as contextuality of each quantum measurement, was practically forgotten. It was highlighted in the works of the author of this paper, with applications both to physics and cognition. In this note, the theory of open quantum systems is applied to formalization of Bohr's contextuality within the the scheme of indirect measurements. This scheme is widely used in quantum information theory and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). In this scheme, Bohr's viewpoint on contextuality of quantum measurements is represented in the formal mathematical framework.