Information-Theoretic Interpretation of Quantum Formalism

Shannon, C. E.: A mathematical theory of communication, Bell System Technical Journal, 27 379–423 , 656–715. (1948), http://pespmc1.vub.ac.be/books/Shannon-TheoryComm.pdf

Szilard, L.: On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings, Zeitschrift fuer Physik, 53 840–856, (1929). http://sns.ias.edu/~tlusty/courses/InfoInBioParis/Papers/Szilard1929.pdf

Brillouin, L.: Science and Information Theory, Academic Press, New-York, (1956). http://www.physics.mcgill.ca/~delrio/courses/phys559/lectures%20and%20notes/Brillouin-Information-Theory-Ch1-4.pdf

Wheeler, J.A.: Information, physics, quantum: the search for links. In: Zurek, W. (ed.) Complexity, entropy, and the physics of information, pp. 3–28. Addison-Wesley, Redwood City (1990)

Landauer, R.: The physical nature of information, Physics Letters A, 217 188–193, (1996). http://cqi.inf.usi.ch/qic/64_Landauer_The_physical_nature_of_information.pdf

Jaynes, E. T.: Probability Theory: the logic of science, Cambridge University Press, Cambridge, UK, (2003). http://omega.math.albany.edu:8008/JaynesBook.html

Jaynes, E. T.: Clearing up mysteries, in: J. Skilling (Ed.), Maximum entropy and Baysian methods, Kluwer, Dordrecht, (1989), pp. 1–29. http://bayes.wustl.edu/etj/articles/cmystery.pdf

Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996). https://doi.org/10.1007/BF02302261

Caves, C.M., Fuchs, C.A., Schack, R.: Quantum probabilities as Bayesian probabilities. Phys. Rev. A 65(2), 22305 (2002). arXiv:quant-ph/0106133

Mermin, N. D.: Qbism puts the scientist back into science, Nature, 507 421–422, (2014). http://www.nature.com/polopoly_fs/1.14912!/menu/main/topColumns/topLeftColumn/pdf/507421a.pdf

Fuchs, C. A.: QBism, The Perimeter of Quantum Bayesianism (2010). arXiv:1003.5209

Boyd, S., Vandenberghe, L.: Convex optimization, Cambridge University Press, Cambridge, (2004). http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf

Cox, R. T.: Probability, frequency, and reasonable expectation, American Journal of Physics, 14 1–13, (1946). http://jimbeck.caltech.edu/summerlectures/references/ProbabilityFrequencyReasonableExpectation.pdf

Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103–1106 (1988)

Frank, R.L., Lieb, E.H.: Entropy and the uncertainty principle. Annales Henri Poincaré 13, 1711–1717 (2012). arXiv:1109.1209

Yeung, R.W.: Information theory and network coding. Springer-Verlag, New York (2008)

Murty, K.G.: Linear programming. Wiley, New York (1983)

Caticha, A.: Lectures on probability, entropy, and statistical physics, In: 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, (2008). arXiv:0808.0012

Feldmann, M.: New loophole for the Einstein-Podolsky-Rozen paradox. Found. Phys. Lett. 8(1), 41–53 (1995). https://doi.org/10.1007/BF02187530. arXiv:quant-ph/9904051

Barrett, J., Linden, N., Massar, S., Pironio, S., Popescu, S., Roberts, D.: Nonlocal correlations as an information-theoretic resource. Phys. Rev. A 71(2), 022101 (2005). arXiv:quant-ph/0404097

Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379 (1994). arXiv:quant-ph/9508009

Birkhoff, G., von Neumann, J.: The logic of quantum mechanics, Annals of Mathematics, 37 823, (1936). http://www.jstor.org/stable/1968621

Jaynes, E. T.: Information theory and statistical mechanics. II, Phys. Rev. 108(2) 170–190, (1957). http://bayes.wustl.edu/etj/articles/theory.2.pdf

Wigner, E. P.: Normal form of antiunitary operators, J. Math. Phys. 1(5) 409–413, (1960). https://link.springer.com/chapter/10.1007/978-3-662-02781-3_38

Durt, T., Englert, B.-G., Bengtsson, I., Zyczkowski, K.: On mutually unbiased bases. Int. J. Quantum Info. 8, 535–640 (2010). arXiv:1004.3348

Kalev, A., Gour, G.: Mutually unbiased measurements in finite dimensions, New Journal of Physics, 16(5), 053038 (2014). arXiv:1401.2706. http://stacks.iop.org/1367-2630/16/i=5/a=053038

Schwinger, J.: Unitary Operator Bases, Proc. Nat. Acad. Sci. USA. 46, 560 (1960). http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=222876 &blobtype=pdf

Wiener, N.: The role of the observer, Philosophy of Science, 3(3), 307–319 (1936). http://www.jstor.org/stable/184668

Feynman, R., Weinberg, S.: Elementary particle physics and the laws of physics. Gen. Relativ. Gravitat. 33, 615–616 (1986)

Klein, F.: A comparative review of recent researches in geometry, Gesammelte mathematische Abhandlungen, 1, 460–497 (1931). arXiv:0807.3161. http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN243240503 &DMDID=dmdlog45

Zuber, J.-B.: Invariances in physics and group theory, In: Conference “Lie and Klein; the Erlangen program and its impact on mathematics and physics”, Strasbourg, Sept. 2012, (2013). arXiv:1307.3970

Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 400(1818), 97–117 (1985). https://people.eecs.berkeley.edu/~christos/classics/Deutsch_quantum_theory.pdf

Gray, J.: Plato’s Ghost: the modernist transformation of mathematics. Princeton University Press, Princeton (2008)

Bouleau, N.: La jonction entre la théorie du potentiel et les probabilités, Cahiers du séminaire d’histoire des mathématiques, 8, 43–66 (1987). http://www.numdam.org/article/CSHM_1987__8__43_0.pdf

Meyer, P.-A., Dellacherie, C.: Probabilité et potentiel, vol. 1 and 2, Hermann, Paris, 1975, (2008)

Hiley, B. J.: Process and the implicate order: their relevance to quantum theory and mind. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.357.4976 &rep=rep1 &type=pdf

Aerts, D., Gabora, L., Sozzo, S., Veloz, T.: Quantum structure in cognition: Fundamentals and applications, In: V. Privman, V. Ovchinnikov (Eds.), Proceedings of the Fifth International Conference on Quantum, Nano and Micro Technologies (ICQMN 2011), International Academy, Research and Industry Association, (2011), pp. 57–62. arXiv:1104.3344

Busemeyer, J.R., Bruza, P.D.: Quantum models of cognition and decision. Cambridge University Press, Cambridge (2012)

Bruza, P., Busemeyer, J., Gabora, L.: Introduction to the Special Issue on Quantum Cognition (2013). arXiv:1309.5673

Dzhafarov, E.N., Kujala, J.V.: Selectivity in probabilistic causality: where psychology runs into quantum physics. J. Math. Psychol. 56, 54–63 (2012). arXiv:1110.2388

Dzhafarov, E.N., Kujala, J.V.: Quantum entanglement and the issue of selective influences in psychology: an overview. Lecture Notes Comput. Sci. 7620, 184–195 (2012). arXiv:1209.0041

Haven, E., Khrennikov, A.: Quantum Soc. Sci. Cambridge University Press, Cambridge (2013)

Clark, S., Coecke, B., Grefenstette, E., Pulman, S., Sadrzadeh, M.: A quantum teleportation inspired algorithm produces sentence meaning from word meaning and grammatical structure (2013). arXiv:1305.0556

Ionicioiu, R.: Quantum mechanics: Knocking at the gates of mathematical foundations, In: I. Parvu, G. Sandu, I. Toader (Eds.), Romanian Studies in Philosophy of Science, Vol. 313 of Boston Studies in the Philosophy and History of Science, Springer, (2015). arXiv:1506.04511

Einstein, A., Born, M.: The Born-Einstein letters. Walker and Company, New-York (1971)

Feynman, R.: Lessons on Probability and Uncertainty in quantum mechanics, Cornell Messenger Lecture Archive, (2011)

Fuchs, C.A.: Quantum mechanics as quantum information (and only a little more). In: Khrennikov, A. (ed.) Quantum Theory: Reconsideration of Foundations, pp. 463–543. Växjö University Press, Växjö, Sweden (2002) . arXiv:quant-ph/0205039

Articles, In: J. T. Cushing, A. Fine, S. Goldstein (Eds.), Bohmian Mechanics and Quantum Theory: An Appraisal, Kluwer, Dordrecht, (1996)

Griffiths, R.B., Omnès, R.: Consistent histories and quantum measurements. Phys. Today 52(8), 26–31 (1999)

Cramer, J.G.: An overview of the transactional interpretation of quantum mechanics. Int. J. Theor. Phys. 27, 227–236 (1988)

Ghirardi, G. C., Pearle, P.: Dynamical reduction theories: Changing quantum theory so the statevector represents reality, In: M. F. A. Fine, L. Wessels (Eds.), Proceedings of the Biennial Meeting of the Philosophy of Science Association, Philosophy of Science Association, East Lansing, MI, (1990)

Zurek, W.H.: Decoherence, Einselection and the existential interpretation (The Rough Guide). Phil. Trans. R. Soc. Lond. A 356, 1793–1821 (1998). arXiv:quant-ph/9805065

Grangier, P.: Contextual objectivity: a realistic interpretation of quantum mechanics (2000). arXiv:quant-ph/0012122

Deutsch, D.: The fabric of reality: the science of parallel universes and its implications. Allen Lane, New York (1997)

Vaidman, L.: The many-worlds interpretation of quantum mechanics, In: E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy, Stanford University, Stanford, CA, (2002). http://plato.stanford.edu/entries/qm-manyworlds/

Spekkens, R.W.: Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A 71, 052108 (2005). arXiv:quant-ph/0406166

Chiribella, G., D’Ariano, G.M., Perinotti, P.: Informational derivation of quantum theory. Phys. Rev. A 84(1), 012311 (2011). arXiv:1011.6451

Hardy, L.: Reconstructing quantum theory (2013). arXiv:1303.1538

Moeller, M. P., Masanes, L.: Information-theoretic postulates for quantum theory (2012). arXiv:1203.4516

Masanes, L., Mueller, M.P., Augusiak, R., Perez-Garcia, D.: A digital approach to quantum theory. Proc. Nat. Acad. Sci. USA 110(41), 16373 (2013). arXiv:1208.0493

Chiribella, G., D’Ariano, G. M., Perinotti, P.: Quantum from principles, In: R. Spekkens, G. Chiribella (Eds.), Quantum theory: informational foundations and foils, Springer Verlag, in press. arXiv:1506.00398

Oeckl, R.: A local and operational framework for the foundations of physics. arXiv:1610.09052

Pitowsky, I.: Quantum mechanics as a theory of probability (2005). arXiv:quant-ph/0510095

Janotta, P., Hinrichsen, H.: Generalized probability theories: what determines the structure of quantum theory? J. Phys. A Math. General 47(32), 323001 (2014). arXiv:1402.6562

Pawłowski, M., Paterek, T., Kaszlikowski, D., Scarani, V., Winter, A., Żukowski, M.: Information causality as a physical principle. Nature 461(7267), 1101–1104 (2009)

Barnum, H., Barrett, J., Clark, L.O., Leifer, M., Spekkens, R., Stepanik, N., Wilce, A., Wilke, R.: Entropy and information causality in general probabilistic theories. N. J. Phys. 12, 033024 (2010). arXiv:0909.5075

Caticha, A.: Entropic dynamics: mechanics without mechanism (2017). arXiv:1704.02663

Fuchs, C. A., Schack, R.: Quantum-Bayesian Coherence: The No-Nonsense Version (2013). arXiv:1301.3274

Leifer, M. S., Spekkens, R. W.: Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference (2011). arXiv:1107.5849

De Raedt, H., Katsnelson, M. I., Michielsen, K.: Quantum theory as the most robust description of reproducible experiments (2013). arXiv:1303.4574

Fuchs, C.A., Mermin, N.D., Schack, R.: An introduction to QBism with an application to the locality of quantum mechanics. Am. J. Phys. 82, 749–754 (2014). arXiv:1311.5253