The extended Bloch representation of quantum mechanics: Explaining superposition, interference, and entanglement

An extended Bloch representation of quantum mechanics was recently derived to offer a possible (hidden-measurements) solution to the measurement problem. In this article we use this representation to investigate the geometry of superposition and entangled states, explaining interference effects and entanglement correlations in terms of the different orientations a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), which we show to be particularly suitable for the description of multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description where sub-entities can remain in well-defined states, even when entangled. This means that the completed version of quantum mechanics provided by the extended Bloch representation, where density operators are also considered to be representative of genuine states (providing a complete description), not only offers a pl...

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