The extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics

TL;DR

This paper introduces an extended Bloch representation (EBR) of quantum mechanics that allows pure states to be represented by density operators, providing a new perspective on entanglement and measurement consistent with the Born rule.

Contribution

The paper develops the extended Bloch representation, enabling a unified description of states, measurements, and entanglement within quantum mechanics.

Findings

EBR allows pure states to be represented by density operators.

Measurement interactions are represented within the EBR framework.

Entanglement is consistently described, maintaining the principle of component existence.

Abstract

The quantum formalism can be completed by assuming that a density operator can also represent a pure state. An 'extended Bloch representation' (EBR) then results, in which not only states, but also the measurement-interactions can be represented. The Born rule is obtained as an expression of the subjective lack of knowledge about the measurement-interaction that is each time actualized. Entanglement can also be consistently described in the EBR, as it remains compatible with the principle according to which a composite entity exists only if its components also exist, and therefore are in pure states.