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We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger.
G. Birkhoff and J. V. Neumann: The Logic of Quantum Mechanics , Ann. Math. 37
1936
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J. von Neumann: Mathematical Foundations of Quantum Mechanics (Princeton University Press 1955)
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A. M. Gleason: Measures on the closed subspaces of a Hilbert space , Indiana Univ. Math. J. 6
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G. W. Mackey: Quantum Mechanics and Hilbert Space , Am. Math. Mon. 64
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J. S. Bell: On the problem on hidden variables in quantum mechanics , Rev. Mod. Phys. 38
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L. Hardy: Quantum theory from five reasonable axioms , arXiv preprint quant-ph/0101012 308
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C. M. Caves, C. A. Fuchs, K. K. Manne and J. M. Renes: Gleason-type derivations of the quantum probability rule for generalized measurements , Found. Phys. 34
2004
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H. Granström: Gleason’s theorem , (Master’s thesis, Stockholm University 2006)
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L. Masanes and M. Müller: A derivation of quantum theory from physical requirements , New J. Phys. 13
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M. Oszmaniec, L. Guerini, P. Wittek and A. Acin: Simulating positive-operator-valued measures with projective measurements , Phys. Rev. Lett. 119
2017
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