Derivation of the Born rule from operational assumptions

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to a variety of foundational approaches to quantum mechanics. It also provides a probability rule for state spaces that are not Hilbert spaces.

[1]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[2]  R. Schack,et al.  Quantum probability from decision theory? , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  David Wallace.  Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation , 2003 .

[4]  David Deutsch.  Quantum theory of probability and decisions , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  P. Holland.  The Quantum Theory of Motion , 1993 .

[6]  Physical Review , 1965, Nature.

[7]  Adrian Kent,et al.  AGAINST MANY WORLDS INTERPRETATIONS , 1990 .

[8]  Weber,et al.  Unified dynamics for microscopic and macroscopic systems. , 1986, Physical review. D, Particles and fields.

[9]  M. Redhead.  Incompleteness, nonlocality, and realism , 1987 .

[10]  H. Bandemer.  Savage, L. J.: Foundations of Statistics. Dover Publ., Inc,. New York 1972. 310 S. , 1974 .

[11]  Antony Valentini,et al.  Hidden Variables, Statistical Mechanics and the Early Universe , 2001 .

[12]  David Wallace,et al.  Quantum Probability and Decision Theory, Revisited , 2002 .

[13]  David Wallace,et al.  Everett and structure , 2001 .

[14]  Simon Saunders.  Time, Quantum Mechanics, and Probability , 2004, Synthese.

[15]  Halliwell,et al.  Quantum mechanics of history: The decoherence functional in quantum mechanics. , 1992, Physical review. D, Particles and fields.