The Extended Bloch Representation of Quantum Mechanics. Explaining Superposition, Interference and Entanglement

TL;DR

This paper uses the extended Bloch representation to clarify the geometry of superposition and entanglement in quantum mechanics, providing new insights into measurement and entanglement problems by representing states within a generalized Bloch sphere.

Contribution

It introduces a tensorial approach to SU(N) generators for multipartite systems and shows that entangled states can be described with sub-entities in well-defined states, solving key quantum issues.

Findings

Provides a geometric interpretation of superposition and entanglement effects.

Introduces a tensorial method for describing multipartite systems.

Shows that entangled states can have sub-entities in well-defined pure states.

Abstract

The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states, explaining the interference effects, and the entanglement correlations, in terms of the different orientations that a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), particularly suitable to describe multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description in which the sub-entities can always remain in well-defined states, even when they are entangled. Therefore, the completed version of quantum mechanics provided by the extended Bloch representation, in which the density operators are also representative of pure states, allows to solve not only the well-known measurement problem, but also the lesser-known entanglement problem. This because we no longer need to give up the general physical principle saying that a composite entity exists, and therefore is in a pure state, if and only if its components also exist, and therefore are in well-defined pure states.