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Operational Axioms for Quantum Mechanics | | Giacomo Mauro D’Ariano
; | | Date: |
8 Nov 2006 | | Abstract: | It is shown how it is possible to derive the mathematical formulation of Quantum Mechanics in terms complex Hilbert space starting from a comprehensive definition of "physical experiment" and from five simple Postulates concerning "experimental accessibility and simplicity". It is also shown how from the same Postulates one could derive an algebraic Gelfand-Naimark-Segal (GNS) representation for transformations. The present paper simplifies and sharpen the previous derivation in quant-ph/0603011. 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 definition of the scalar product and of the adjoint. What is new in the present paper with respect to quant-ph/0603011, is the deduction of an involution corresponding to the complex-conjugation, by which we can define the usual complex adjoint. | | Source: | arXiv, quant-ph/0611094 | | Services: | Forum | Review | PDF | Favorites | |
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