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

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