The structure of ordered Banach spaces in axiomatic quantum mechanics

Neumann, Holger

doi:10.1007/3-540-06725-6_13

Cited by 2 publications

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“…In the present attempt some expert readers will recognize similarities with the program of other authors during the seventies, following the Ludwig school [1], which were seeking operational principles to select the structure of quantum states from all possible convex structures [see, for example, the papers of U. Krause [2], H. Neumann [3], and E. Størmer [4] collected in the book [5]]. Why these work didn't have a followup?…”

Section: Introductionmentioning

confidence: 99%

Operational Axioms for Quantum Mechanics

D’Ariano¹

2007

AIP Conference Proceedings

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Abstract. The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an Operational Epistemic Theory. In such context the quantum superposition principle has an extraneous non epistemic nature. This leads us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces.In the present work I present a set of axioms of purely operational nature, based on a general definition of "the experiment", the operational/epistemic archetype of information retrieval from reality. As we will see, this starting point logically entails a series of notions [state, conditional state, local state, pure state, faithful state, instrument, propensity (i.e. "effect"), dynamical and informational equivalence, dynamical and informational compatibility, predictability, discriminability, programmability, locality, a-causality, rank of the state, maximally chaotic state, maximally entangled state, informationally complete propensity, etc. ], along with a set of rules (addition, convex combination, partial orderings, ... ), which, far from being of quantum origin as often considered, instead constitute the universal syntactic manual of the operational/epistemic approach. The missing ingredient is, of course, the quantum superposition axiom for probability amplitudes: for this I propose some substitute candidates of purely operational/epistemic nature.

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