Axioms for Quantum Theory

In General
* Possible set: (adapted from slides by W Zurek)
(1) The universe is made of systems.
(2) Each system has a Hilbert space; The Hilbert space of a composite system is the tensor product of the constituent ones.
(3) A pure state for a system is a vector in the Hilbert space of that system.
(4) The evolution of an isolated system is a unitary transformation on Hilbert space.
(5) Observables are associated with Hermitian operators on Hilbert space.
(6) The only possible outcome of a measurement is an eigenstate (and eigenvalue) of the operator.
(7) Probabilities of various outcomes are given by Born's rule.

References > s.a. causality; quantum information.
@ General: Margenau PR(36) [removal of one postulate]; Piron HPA(64); Fivel pr(73); Landsman qp/96, 98; Ghaboussi qp/98; Hardy qp/00-wd, qp/01 [from classical probability, comment Schack FP(03)qp/02, Duck qp/03, Johnson qp/06]; Aerts qp/01; Khrennikov qp/02-in; Volovich qp/02 [new set]; Minic & Tze PLB(04)ht/03; Sakai qp/04/JMP; Slavnov TMP(05)qp [based on algebra of observables and functionals]; D'Ariano qp/05-in, qp/06-in, qp/06-in, qp/06-in [operational]; Mehrafarin IJTP(05); Parwani IJTP(06); Held a0705; Diego a0801.
@ Quantum-gravity-motivated: Giddings a0711.
@ Auxiliary rules: Mould qp/05, qp/05, qp/06-in [nRules], qp/06 [covariance of nRules].
@ From cryptography: Clifton et al; Smolin qp/03; Halvorson & Bub qp/03.
@ Projection postulate: Ballentine FP(90); Kronz PhSc(92); > s.a. wave function collapse.
@ Linearity: Caticha PLA(98)qp, PRA(98)qp [need]; Aerts & Valckenborgh qp/02-in, qp/02-in [questioning]; Jordan PRA(06)qp/05 [assumptions]; > s.a. Non-Linear Quantum Mechanics.
@ Related topics: Nottale & Célérier JPA(07)-a0711 [from principles of scale relativity].

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