dorsal/arxiv
View SchemaOn the missing axiom of Quantum Mechanics
| Authors | Giacomo Mauro D'Ariano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506034 |
| URL | https://arxiv.org/abs/quant-ph/0506034 |
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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"abstract": "The debate on the nature of quantum probabilities in relation to Quantum Non\nLocality has elevated Quantum Mechanics to the level of an \"Operational\nEpistemic Theory\". In such context the quantum superposition principle has an\nextraneous non epistemic nature. This leads us to seek purely operational\nfoundations for Quantum Mechanics, from which to derive the current\nmathematical axiomatization based on Hilbert spaces.\n In the present work I present a set of axioms of purely operational nature,\nbased on a general definition of \"the experiment\", the operational/epistemic\narchetype of information retrieval from reality. As we will see, this starting\npoint logically entails a series of notions [state, conditional state, local\nstate, pure state, faithful state, instrument, propensity (i.e. \"effect\"),\ndynamical and informational equivalence, dynamical and informational\ncompatibility, predictability, discriminability, programmability, locality,\na-causality, rank of the state, maximally chaotic state, maximally entangled\nstate, informationally complete propensity, etc. ], along with a set of rules\n(addition, convex combination, partial orderings, ...), which, far from being\nof quantum origin as often considered, instead constitute the universal\n\"syntactic manual\" of the operational/epistemic approach. The missing\ningredient is, of course, the quantum superposition axiom for probability\namplitudes: for this I propose some substitute candidates of purely\noperational/epistemic nature.",
"arxiv_id": "quant-ph/0506034",
"authors": [
"Giacomo Mauro D\u0027Ariano"
],
"categories": [
"quant-ph"
],
"title": "On the missing axiom of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0506034"
},
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