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

The extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics