The Extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics

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.

Using Abstract Elastic Membranes to Learn About Quantum Measurements

“…In [7], the EBR and HMI are also compared with the transactional interpretation, particularly concerning the possibility of understanding a quantum measurement as weighted symmetry breaking process. Let us mention that the EBR allows to clarify and demistify other quantum phenomena, like entanglement, showing that it remains compatible with the principle according to which a composite entity exists only if its components also exist, and therefore are in well-defined states [8,9]. Finally, we point out that some nice computer animations of the unfolding of a measurement in the EBR, for the N = 2, 3, 4 situations, can be found in [10].…”

A remark on quantum cloning

“…However, we also observed that there is no discussion in the literature, or in textbooks (as far as we can judge) about the rather obvious fact that cloning, as a notion, refers primarily to a physical entity, not to its state. Quantum elementary entities being truly and strikingly indiscernible, they are always the perfect physical clones of one another, and as soon as they are allowed to interact, they become perfect copies of one another also for what concerns their individual states, at least for as long as one accepts to complete standard quantum mechanics by also including operator-states as a description of genuine individual states [12].…”