Where the mathematical structure of quantum mechanics comes from

Beyond the Quantum

Volumn , Issue , 2007, Pages 191-202

  D'Ariano G M ^a,b  

^a UNIVERSITY OF PAVIA   (Italy)

^b Northwestern University   (United States)

Author keywords

Axiomatics; Banach spaces; C* algebras; Hilbert spaces; Quantum Mechanics

Indexed keywords

EID: 84968835207     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812771186_0016     Document Type: Chapter

References (10)

1. G. M. D’Ariano, How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms, work presented at the conference On the Present Status of Quantum Mechanics held on 7-9 September 2005, Mali Losinj, Croatia, in celebration of the 70th birthday of Gian Carlo Ghirardi. Also in quant-ph/0603011.
2. G. M. D’Ariano, Quantum Theory, Reconsideration of Foundations - 3, Va{double acute}xjő, Sweden, 6-11 June 2005, edited by G. Adenier, A. Y. Khrennikov, and Th. M. Nieuwenhuizen, (American Institute of Physics, Melville, New York, 2006). Also in quant-ph/0506034.
3. G. M. D’Ariano, in Foundations of Probability and Physics-4, Quantum Theory: Reconsideration of Foundations-3, Va{double acute}xjő, Sweden, 4-9 June 2006, edited by G. Adenier, A. Y. Khrennikov, and Th. M. Nieuwenhuizen, (American Institute of Physics, Melville, New York, 2007). Also in quant-ph/0611094.
4. I. M. Gelfand, and M. A. Neumark, Mat. Sb. 12, 197 (1943).
5. G. Ludwig, An Axiomatic Basis for Quantum Mechanics I: Derivation of Hilbert Space Structure, (Springer, SPR:adr, 1985).
6. G. M. D’Ariano, Tomographic methods for universal estimation in quantum optics, (IOS Press, Amsterdam, 2002), pp. 385-406, scuola "E. Fermi" on Experimental Quantum Computation and Information.
7. G. M. D’Ariano, P. L. Presti, and L. Maccone, Phys. Rev. Lett. 93, 250407 (2004).
8. G. M. D’Ariano, and P. L. Presti, Phys. Rev. Lett. 86, 4195 (2001).
9. G. M. D’Ariano, and P. L. Presti, Phys. Rev. Lett. 91, 047902-1-4 (2003).
10. P. Busch, Phys. Rev. Lett. 91 120403 (2003).