Relational Quantum Mechanics and Probability

Bohr, N.: On the constitution of atoms and molecules. Philos. Mag. 26, 476–502 (1913)

Feynman, R.: The Character of Physical Law. MIT Press, Cambridge (1967)

Auletta, G.: Foundations and Interpretation of Quantum Mechanics: In the Light of a Critical–Historical Analysis of the Problems and of a Synthesis of the Results. World Scientific, Singapore (2001)

Hardy, L.: Quantum theory from five reasonable axioms. arXiv preprint arxiv:quant-ph/0101012 (2001)

Clifton, R., Bub, J., Halvorson, H.: Characterizing quantum theory in terms of information-theoretic constraints. Found. Phys. 33, 1561–1591 (2003)

Grinbaum, A.: Reconstruction of quantum theory. Br. J. Philos. Sci. 58, 387–408 (2007)

Grinbaum, A.: Reconstructing instead of interpreting quantum theory. Philos. Sci. 74, 761–774 (2007)

Dakic, B., Brukner, C.: Quantum theory and beyond: Is entanglement special? arXiv preprint arXiv:0911.0695 (2009)

Hohenberg, P.C.: Colloquium: an introduction to consistent quantum theory. Rev. Mod. Phys. 82, 2835–2844 (2010)

Chiribella, G., D’Ariano, G.M., Perinotti, P.: Informational derivation of quantum theory. Phys. Rev. A 84, 012311 (2011)

Fuchs, C.A., Schack, R.: Quantum-Bayesian coherence. Rev. Mod. Phys. 85, 1693–1715 (2013)

Masanes, L., Müller, M.P., Augusiak, R., Pèrez-Garcìa, D.: Existence of an information unit as a postulate of quantum theory. Proc. Natl. Acad. Sci. USA 110, 16373–16377 (2013)

Barnum, H., Müller, M.P., Ududec, C.: Higher-order interference and single-system postulates characterizing quantum theory. New J. Phys. 16, 123029 (2014)

Dickson, M.: Reconstruction and reinvention in quantum theory. Found. Phys. 45, 1330–1340 (2015)

Auffèves, A., Grangier, P.: Contexts, systems and modalities: a new ontology for quantum mechanics. Found. Phys. 46, 121–137 (2016)

Friedberg, R., Hohenberg, P.C.: What is quantum mechanics? A minimal formulation. Found. Phys. 48, 295–332 (2018)

Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996)

Brukner, C., Zeilinger, A.: Operationally invariant information in quantum measurements. Phys. Rev. Lett. 83, 3354–3357 (1999)

Brukner, C., Zeilinger, A.: Young’s experiment and the finiteness of information. Philos. Trans. R. Soc. A 360, 1061–1069 (2002)

Fuchs, C.A.: Quantum mechanics as quantum information (and only a little more). arXiv preprint arxiv:quant-ph/0205039 (2002)

Barrett, J.: Information processing in generalized probabilistic theories. Phys. Rev. A 75, 032304 (2007)

Brukner, C., Zeilinger, A.: Information invariance and quantum probabilities. Found. Phys. 39, 677–689 (2009)

Höhn, P.A., Wever, C.S.P.: Quantum theory from questions. Phys. Rev. A 95, 012102 (2017)

Höhn, P.: Toolbox for reconstructing quantum theory from rules on information acquisition. Quantum 1, 38 (2017)

Höhn, P.: Quantum theory from rules on information acquisition. Entropy 19, 98 (2017)

Yang, J.: Quantum mechanics from relational properties, Part I: Formulation. arXiv preprint arXiv:1706.01317 (2017)

Yang, J.: Quantum mechanics from relational properties, Part II: Measurement. arXiv preprint arXiv:1803.04843 (2018)

Yang, J.: Quantum mechanics from relational properties, Part III: Path integral implementation. arXiv preprint arXiv:1807.01583 (2018)

Smerlak, M., Rovelli, C.: Relational EPR. Found. Phys. 37, 427–445 (2007)

Rovelli, C.: Space is blue and birds fly through it. Philos. Trans. R. Soc. A. 376, 0312 (2018)

Poulin, D.: Toy model for a relational formulation of quantum theory. Int. J. Theor. Phys. 45, 1189–1215 (2006)

Brown, M.J.: Relational quantum mechanics and the determinacy problem. Br. J. Philos. Sci. 60, 679–695 (2009)

van Fraassen, B.C.: Rovelli’s world. Found. Phys. 40, 390–417 (2009)

Grinbaum, A.: Information-theoretic princple entails orthomodularity of a lattice. Found. Phys. Lett. 18, 563–572 (2005)

Birkhoff, G., Von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823–843 (1936)

Von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)

Beltrametti, E., Cassinelli, G.: The Logic of Quantum Mechanics. Cambridge University Press, Cambridge (1984)

Hughes, R.: The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Cambridge (1989)

Dalla Chiara, M., Giuntini, R., Greechie, R.: Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics. Springer, Dordrecht (2004)

Cohen-Tannoudji, C., Diu, B., Laloë, F.: Mècanique Quantique, 2nd edn. Hermann, Paris (1996)

Hájek, A.: Interpretations of probability. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Stanford (2012)

Fine, T.: Theories of Probability: An Examination of Foundations. Academic Press, Cambridge (1973)

Kolmogorov, A.: Foundations of the Theory of Probability. Chelsea Pub. Co, New York (1956)

Jaynes, E., Bretthorst, G.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)

Gudder, S.: Quantum Probability. Academic Press, New York (1988)

Varadarajan, V.: Geometry of Quantum Theory. Springer, New York (2007)

Cox, R.: Algebra of Probable Inference. Johns Hopkins University Press, Baltimore (1961)

Ballentine, L.E.: Probability theory in quantum mechanics. Am. J. Phys. 54, 883–889 (1986)

Ballentine, L.E.: Propensity, probability, and quantum theory. Found. Phys. 46, 973–1005 (2016)

Auffèves, A., Grangier, P.: Recovering the quantum formalism from physically realist axioms. Sci. Rep. 7, 43365 (2017)

Gleason, A.M.: Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885–893 (1957)

Piron, C.: Survey of general quantum physics. Found. Phys. 2, 287–314 (1972)

Piron, C.: Foundations of Quantum Physics. Benjamin-Cummings Publishing Company, San Francisco (1976)

Cox, R.T.: Probability, frequency and reasonable expectation. Am. J. Phys. 14, 1–13 (1946)

D’Agostini, G.: Bayesian Reasoning in Data Analysis: A Critical Introduction. World Scientific, Singapore (2003)

Feynman, R.P.: The concept of probability in quantum mechanics. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley (1951)

Bergmann, M.: An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press, Cambridge (2008)