dorsal/arxiv
View SchemaOperational Axioms for Quantum Mechanics
| Authors | Giacomo Mauro D'Ariano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611094 |
| URL | https://arxiv.org/abs/quant-ph/0611094 |
Abstract
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of "physical experiment" and from five simple Postulates concerning "experimental accessibility and simplicity". For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in version 1. The main ingredient of the axiomatization is the postulated existence of "faithful states" that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the "transposed" of a physical transformation. What is new in the present paper with respect to quant-ph/0603011 is the operational deduction of an involution corresponding to the "complex-conjugation" for effects, whose extension to transformations allows to define the "adjoint" of a transformation when the extension is composition-preserving.
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"abstract": "The mathematical formulation of Quantum Mechanics in terms of complex Hilbert\nspace is derived for finite dimensions, starting from a general definition of\n\"physical experiment\" and from five simple Postulates concerning \"experimental\naccessibility and simplicity\". For the infinite dimensional case, on the other\nhand, a C*-algebra representation of physical transformations is derived,\nstarting from just four of the five Postulates via a Gelfand-Naimark-Segal\n(GNS) construction. The present paper simplifies and sharpens the previous\nderivation in version 1. The main ingredient of the axiomatization is the\npostulated existence of \"faithful states\" that allows one to calibrate the\nexperimental apparatus. Such notion is at the basis of the operational\ndefinitions of the scalar product and of the \"transposed\" of a physical\ntransformation. What is new in the present paper with respect to\nquant-ph/0603011 is the operational deduction of an involution corresponding to\nthe \"complex-conjugation\" for effects, whose extension to transformations\nallows to define the \"adjoint\" of a transformation when the extension is\ncomposition-preserving.",
"arxiv_id": "quant-ph/0611094",
"authors": [
"Giacomo Mauro D\u0027Ariano"
],
"categories": [
"quant-ph"
],
"title": "Operational Axioms for Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0611094"
},
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