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Quantum Theory from First Principles
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Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. It is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.


‘An extraordinary book on the deep principles behind quantum theory.'

Nicolas Gisin - Université de Genève

‘Part quantum mechanics textbook, part original research contribution, this book is a fascinating, audacious effort to ‘rebuild quantum mechanics from the ground up', presenting it as the logical consequence of simple information-theoretic postulates. Students wishing to learn quantum information should read it and do all the exercises!'

Scott Aaronson - Massachusetts Institute of Technology

'From the earliest days of quantum theory to the present, physicists have been pleased with the excellent results it yields but also unsettled (in varying degrees) by the fact that its mathematical forms do not always have clear physical interpretations. Some efforts to resolve this problem in recent decades have focused on replacing mathematical postulates with informational postulates. The authors take this approach here … [intended for] not just physicists but also mathematicians and computer scientists. The first section, about one-third of the book's length, is flagged by the authors as suitable for an undergraduate course and might well serve so at the highest undergraduate levels … The two remaining sections are aimed at a master's-level audience; the final section lays out the derivation of quantum theory from six informational principles … A generous number (more than 200) practice exercises are included, with solutions available for selected problems.'

K. D. Fisher Source: Choice

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Aharonov, D., Kitaev, A., and Nisan, N. 1998. Quantum circuits with mixed states. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC). New York, NY: ACM.
Aharonov, Y., Anandan, J., and Vaidman, L. 1993. Meaning of the wave function. Phys. Rev. A, 47, 4616–4626.
Aharonov, Y. and Vaidman, L. 1993. Measurement of the Schrödinger wave of a single particle. Phys. Lett. A, 178, 38–42.
Alfsen, E. M. and Shultz, F. W. 2001. State Spaces of Operator Algebras: Basic Theory, Orientations, and C*-products. Boston, MA: Birkhäuser.
Alfsen, E. M. and Shultz, F. W. 2003. Geometry of State Spaces of Operator Algebras. Boston, MA: Birkhäuser.
Alicki, R. and Lendi, K. 1987. Quantum Dynamical Semigroups and Applications. Lecture Notes in Physics, vol. 286. Berlin: Springer.
Alter, O. and Yamamoto, Y. 1995. Inhibition of the measurement of the wave function of a single quantum system in repeated weak quantum nondemolition measurements. Phys. Rev. Lett., 74, 4106–4109.
Araki, H. 1980. On a characterization of the state space of quantum mechanics. Comm. Math. Phys., 75(1), 1–24.
Barnum, H., Nielsen, M. A., and Schumacher, B. 1998. Information transmission through a noisy quantum channel. Phys. Rev. A, 57, 4153–4175.
Barnum, H., Gaebler, C. P., and Wilce, A. 2009. Ensemble steering, weak self-duality, and the structure of probabilistic theories. arXiv, quant-ph.
Barnum, H., Mueller, M. P., and Ududec, C. 2014. Higher-order interference and singlesystem postulates characterizing quantum theory. arXiv:1403.4147.
Barrett, J. 2007. Information processing in generalized probabilistic theories. Phys. Rev. A, 75(3), 032304.
Barvinok, A. 2002. A Course in Convexity. Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
Baumeler, Ä. and Wolf, S. 2015. Device-independent test of causal order and relations to fixed-points.
Belavkin, V. P. and Staszewski, P. 1986. A Radon Nikodym theorem for completely positive maps. Rep. Math. Phys., 24, 49–53.
Belavkin, V. P., D'Ariano, G. M., and Raginsky, M. 2005. Operational distance and fidelity for quantum channels. J. Math. Phys., 46(6), 062106.
Béllissard, J. and Iochum, B. 1978. Homogeneous self-dual cones, versus Jordan algebras: the theory revisited. Ann. Inst. Fourier (Grenoble), 28(1), v, 27–67.
Beltrametti, E. G., Cassinelli, G., Rota, G.-C., and Carruthers, P. A. 2010. The Logic of Quantum Mechanics. Vol. 15. Cambridge: Cambridge University Press.
Bennett, C. H. and Wiesner, S. J. 1992. Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. lett., 69(20), 2881.
Bennett, C. H., Brassard, G., et al. 1984. Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, vol. 175. New York: IEEE.
Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., and Wootters, W. K. 1993. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 70(13), 1895.
Bennett, C. H., Bernstein, H. J., Popescu, S., and Schumacher, B. 1996. Concentrating partial entanglement by local operations. Phys. Rev. A, 53, 2046.
Bernstein, E. and Vazirani, U. 1993. Quantum complexity theory. Pages 11–20 of: Proceedings of the Twenty-fifth Annual ACM Symposium on Theory of Computing. New York, NY: ACM.
Bhatia, R. 1997. Matrix Analysis. New York: Springer-Verlag.
Birkhoff, G. 1984. Lattice theory. In: Dilworth, R. P. (ed.), Proceedings of the Second Symposium in Pure Mathematics of the American Mathematical Society April 1959, vol. 175. Providence, RI: American Mathematical Society.
Birkhoff, G. and von Neumann, J. 1936. The logic of quantum mechanics. Math. Annal., 37, 823.
Bisio, A., Chiribella, G., D'Ariano, G. M., Facchini, S., and Perinotti, P. 2009a. Optimal quantum tomography. IEEE J. Select. Topics Quantum Elec., 15(6), 1646.
Bisio, A., Chiribella, G., D'Ariano, G. M., Facchini, S., and Perinotti, P. 2009b. Optimal quantum tomography of states, measurements, and transformations. Phys. Rev. Lett., 102(1), 010404.
Bisio, A., Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2012. Quantum networks: general theory and applications. Acta Phys. Slovaca, 61(1), 273–390.
Brandenburger, A. and Yanofsky, N. 2008. A classification of hidden-variable properties. J. Phys. A, 41(42), 425302.
Brassard, G. 2005. Is information the key? Nature Phys., 1(1), 2–4.
Brukner, C. 2014a. Bounding quantum correlations with indefinite causal order.
Brukner, C. 2014b. Quantum causality. Nature Phys., 10(4), 259–263.
Bruss, D., D'Ariano, G. M., Macchiavello, C., and Sacchi, M. F. 2000. Approximate quantum cloning and the impossibility of superluminal information transfer. Phys. Rev. A, 62(6), 062302.
Buscemi, F., D'Ariano, G. M., and Perinotti, P. 2004. There exist nonorthogonal quantum measurements that are perfectly repeatable. Phys. Rev. Lett., 92, 070403.
Buscemi, F., Chiribella, G., and D'Ariano, G. M. 2005. Inverting quantum decoherence by classical feedback from the environment. Phys. Rev. Lett., 95, 090501.
Busch, P., Lahti, P. J., and Mittelstaedt, P. 1991. The Quantum Theory of Measurement. Berlin: Springer.
Childs, A. M., Chuang, I. L., and Leung, D. W. 2001. Realization of quantum process tomography in NMR. Phys. Rev. A, 64(Jun), 012314.
Chiribella, G. and Spekkens, R. (eds). 2015. Quantum Theory: Informational Foundations and Foils. Japan: Springer Verlag.
Chiribella, G., D'Ariano, G. M., and Schlingemann, D. 2007. How continuous quantum measurements in finite dimensions are actually discrete. Phys. Rev. Lett., 98(19), 190403.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2008a. Quantum circuit architecture. Phys. Rev. Lett., 101(6), 060401.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2008b. Optimal cloning of unitary transformation. Phys. Rev. Lett., 101, 180504.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2008c. Quantum circuit architecture. Phys. Rev. Lett., 101, 060401.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2009. Theoretical framework for quantum networks. Phys. Rev. A, 80(2), 022339.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2010a. Probabilistic theories with purification. Phys. Rev. A, 81(6), 062348.
Chiribella, G., D'Ariano, G. M., and Schlingemann, D. 2010b. Barycentric decomposition of quantum measurements in finite dimensions. J. Math. Phys., 51(2), 022111.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2010c. Probabilistic theories with purification. Phys. Rev. A, 81(6), 062348.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2011. Informational derivation of quantum theory. Phys. Rev. A, 84(1), 012311.
Chiribella, G., D'Ariano, G. M., Perinotti, P., and Valiron, B. 2013a. Quantum computations without definite causal structure. Phys. Rev. A, 88(Aug), 022318.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2013b. A short impossibility proof of quantum bit commitment. Phys. Lett. A, 377, 1076–1087.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2014. Non-causal theories with purification. arxiv.
Chiribella, G., D'Ariano, G. M., and Perinotti, P. 2015. Non-causal theories with purification. in preparation.
Choi, M.-D. 1972. Positive linear linear maps on C* algebras. Canad. J. Math., XXIV(3), 520–529.
Choi, M.-D. 1975. Completely positive linear maps on complex matrices. Linear Algebra Appl., 10, 285–290.
Chuang, I. L. and Nielsen, M. A. 2000. Quantum Information and Quantum Computation. Cambridge: Cambridge University Press.
Clifton, R., Bub, J., and Halvorson, H. 2003. Characterizing quantum theory in terms of information-theoretic constraints. Foundations of Phys., 33(11), 1561–1591.
Coecke, B. 2008. Introducing categories to the practicing physicist. Adv. Stud. Math. Logic, 30, 45.
Coecke, B. 2006. Introducing categories to the practicing physicist. Pages 289–355 of: What is Category Theory? Advanced Studies in Mathematics and Logic, vol. 30. Milan, Italy: Polimetrica Publishing.
Coecke, B., Moore, D., and Wilce, A. 2000. Current research in operational quantum logic: algebras, categories, languages. Vol. 111. New York: Springer Science & Business Media.
Cox, R. T. 1961. The Algebra of Probable Inference. Baltimore, OH: Johns Hopkins University.
Dakic, B. and Brukner, C. 2011. Quantum theory and beyond: is entanglement special? Pages 365–392 of: Halvorson, H. (ed.), Deep Beauty: Understanding the Quantum World through Mathematical Innovation. Cambridge University Press.
D'Ariano, G. M. 1997. Homodyning as universal detection. Pages 365–392 of: Hirota, O., Holevo, A. S., and Caves, C. M. (eds), Quantum Communication, Computing and Measurement. New York and London: Plenum.
D'Ariano, G. M. 2005. Homodyning as universal detection. Pages 494–508 of: Hayashi, M. (ed.), Asymptotic Theory of Quantum Statistical Inference, Selected Papers. Singapore: World Scientific.
D'Ariano, G. M. 2006a. How to derive the Hilbert-space formulation of quantum mechanics from purely operational axioms. In: Bassi, A., Duerr, D., Weber, T., and Zanghi, N. (eds), Quantum Mechanics, vol. 844. USA: American Institute of Physics.
D'Ariano, G. M. 2006b. On the missing axiom of Quantum Mechanics. Pages 114–130 of: AIP Conference Proceedings, vol. 810.
D'Ariano, G. M. 2007a. Operational axioms for a C*,-algebraic formulation for Quantum Mechanics. Page 191 of: Hirota, O., Shapiro, J. H., and Sasaki, M. (eds), Proceedings of the 8th Int. Conf. on Quantum Communication, Measurement and Computing. Japan: NICT press.
D'Ariano, G. M. 2007b. Operational axioms for quantum mechanics. Page 79 of: Adenier, G., Fuchs, C. A., and Khrennikov, A. Yu. (eds), AIP Conference Proceedings, vol. 889. USA: American Institute of Physics.
D'Ariano, G. M. 2010. Probabilistic theories: what is special about quantum mechanics? Chap. 5 of: Bokulich, A. and Jaeger, G. (eds), Philosophy of Quantum Information and Entanglement. Cambridge: Cambridge University Press.
D'Ariano, G. M. and Lo Presti, P. 2001. Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. Phys. Rev. Lett., 86(May), 4195–4198.
D'Ariano, G. M. and Lo Presti, P. 2003. Imprinting a complete information about a quantum channel on its output state. Phys. Rev. Lett., 91, 047902.
D'Ariano, G. M. and Perinotti, P. 2005. Efficient universal programmable quantum measurements. Phys. Rev. lett., 94(9), 090401.
D'Ariano, G. M. and Perinotti, P. 2007. Optimal data processing for quantum measurements. Phys. Rev. Lett., 98, 020403.
D'Ariano, G. M. and Tosini, A. 2010. Testing axioms for quantum theory on probabilistic toy-theories. Quantum Inf. Proc., 9, 95–141.
D'Ariano, G. M. and Tosini, A. 2013. Emergence of space-time from topologically homogeneous causal networks. Studies in History and Philosophy of Modern Physics.
D'Ariano, G. M. and Yuen, H. P. 1996. Impossibility of measuring the wave function of a single quantum system. Phys. Rev. Lett., 76(Apr), 2832–2835.
D'Ariano, G. M., Macchiavello, C., and Paris, M. G. A. 1994. Detection of the density matrix through optical homodyne tomography without filtered back projection. Phys. Rev. A, 50(Nov), 4298–4302.
D'Ariano, G. M., Lo Presti, P., and Sacchi, M. 2000. Bell measurements and observables. Phys. Lett. A, 272, 32.
D'Ariano, G. M., Lo Presti, P., and Perinotti, P. 2005. Classical randomness in quantum measurements. J. Phys. A: Math. Gen., 38(26), 5979–5991.
D'Ariano, G. M., Giovannetti, V., and Perinotti, P. 2006. Optimal estimation of quantum observables. J. of Math. Phys., 47, 022102–1.
D'Ariano, G. M., Kretschmann, D., Schlingemann, D., and Werner, R. F. 2007. Reexamination of quantum bit commitment: the possible and the impossible. Phys. Rev. A, 76, 032328.
D'Ariano, G. M., Manessi, F., and Perinotti, P. 2014a. Determinism without causality. Physica Scripta, T163, 014013.
D'Ariano, G. M., Manessi, F., Perinotti, P., and Tosini, A. 2014b. Fermionic computation is non-local tomographic and violates monogamy of entanglement. EPL (Europhysics Letters), 107(2), 20009.
Davies, E. B. 1977. Quantum dynamical semigroups and the neutron diffusion equation. Rep. Math. Phys., 11, 169.
Dieks, D. G. B. J. 1982. Communication by EPR devices. Phys. Lett. A, 92(6), 271–272.
Dowe, P. 2007. Physical Causation. Cambridge Studies in Probability, Induction and Decision Theory. Cambridge: Cambridge University Press.
Eberhard, P. H. 1978. Bell's theorem and the different concepts of locality. Il Nuovo Cimento B Series 11, 46(2), 392–419.
Einstein, A., Podolsky, B., and Rosen, N. 1935. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47(10), 777–780.
Ekert, A. K. 1991. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett., 67(6), 661.
Ellis, G. F. R. 2008. On the flow of time. arXiv preprint arXiv:0812.0240.
Feynman, R. 1965. The Character of Physical Law. London: BBC Books.
Foulis, D. J. and Randall, C. H. 1984. A note on misunderstandings of Piron's axioms for quantum mechanics. Found. Phys., 14, 65–88.
Foulis, D. J., Piron, C., and Randall, C. H. 1983. Realism, operationalism, and quantum mechanics. Found. Phys., 13, 813–841.
Fuchs, C. A. 2002. Quantum mechanics as quantum information (and only a little more). arXiv preprint quant-ph/0205039.
Fuchs, C. A. 2003. Quantum mechanics as quantum information, mostly. J. of Modern Optics, 50(6-7), 987–1023.
Fuchs, C. A. and Schack, R. 2013. Quantum-Bayesian coherence. Rev. Mod. Phys., 85, 1693–1715.
Fuchs, C. A., et al. 2001. Quantum foundations in the light of quantum information. NATO Science Series Sub Series III Comp. Syst. Sci., 182, 38–82.
Ghirardi, G.-C., Rimini, A., and Weber, T. 1980. A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere Al Nuovo Cimento (1971–1985), 27(10), 293–298.
Gillies, D. 2000. Philosophical Theories of Probability. Move Psychology Press.
Gordon, J. P. and Louisell, W. H. 1966. Simultaneous measurements of noncommuting observables. Phys. of Quantum Elec., 1, 833–840.
Gorini, V., Kossakowski, A., and Sudarshan, E. C. G. 1976. Completely positive dynamical semigroups of N-level systems. J. Math. Phys., 17, 821.
Goyal, P., Knuth, K. H., and Skilling, J. 2010. Origin of complex quantum amplitudes and Feynman's rules. Phys. Rev. A, 81(Feb), 022109.
Gregoratti, M. and Werner, R. F. 2003. Quantum lost and found. Journal of Modern Optics, 50(6-7), 915–933.
Gross, D., Müller, M., Colbeck, R., and Dahlsten, O. C. O. 2010. All reversible dynamics in maximally nonlocal theories are trivial. Phys. Rev. Lett., 104(Feb), 080402.
Grover, L. K. 1996. A fast quantum mechanical algorithm for database search. Pages 212–219 of: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing. STOC–96. New York, NY: ACM.
Haag, R. 1993. Local Quantum Physics. Berlin: Springer-Verlag.
Haag, R. and Haag, R. 1996. Local Quantum Physics: Fields, Particles, Algebras, Vol. 2. Berlin: Springer.
Hardy, L. 2001. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012.
Hardy, L. 2011. Reformulating and reconstructing quantum theory. quant-ph, Apr.
Hardy, L. and Wootters, W. K. 2012. Limited holism and real-vector-space quantum theory. Found. Phys., 42(3), 454–473.
Heisenberg, W. 1930. The Physical Principles of the Quantum Theory. Trans. C., Eckart and F. C., Hoyt. Chicago, IL: Chicago University Press.
Helstrom, C. W. 1976. Quantum Detection and Estimation Theory.Mathematics in Science and Engineering, Vol. 123. New York NY: Academic Press.
Herbert, N. 1982. FLASH – A superluminal communicator based upon a new kind of quantum measurement. Found. Phys., 12, 1171.
Hilbert, D., von Neumann, J., and Nordheim, L. 1928. Über die Grundlagen der Quantenmechanik. Mathematische Annalen, 98(1), 1–30.
Holevo, A. S. 1982. Probabilistic and Statistical Aspects of Quantum Theory. Series in Statistics and Probability, vol. 1. Amsterdam: North-Holland.
Holevo, A. S. 2011. The Choi–Jamiolkowski forms of quantum Gaussian channels. J. Math. Phys., 52(4), 042202.
Horodecki, M., Horodecki, P., and Horodecki, R. 1996. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 223, 1–8.
Imamoglu, A. 1993. Logical reversibility in quantum-nondemolition measurements. Phys. Rev. A, 47, R4577–R4580.
Jamiolkowski, A. 1972. Linear transformations which preserve trace and positive semidefiteness of operators. Rep. Math. Phys., 3, 275.
Jauch, J. M. and Piron, C. 1963. Can hidden variables be excluded in quantum mechanics? Helv. Phys. Acta, 36, 827.
Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press.
Johnson, D. and Feige, U. (eds) 2007. Toward a General Theory of Quantum Games. Vol. STOC–07 Symposium on Theory of Computing Conference. New York, NY: ACM.
Jordan, P., von Neumann, J., and Wigner, E. 1934. On an algebraic generalization of the quantum mechanical formalism. Ann. Math., 35, 29.
Joyal, A. and Street, R. 1991. The geometry of tensor calculus, I. Adv. Math., 88(1), 55–112.
Kaiser, D. 2011. How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival. New York: WW Norton & Company.
Kato, T. 1980. Perturbation Theory for Linear Operators. New York, NY: Springer.
Keynes, J. M. 2004. A Treatise on Probability. Dover Books on Mathematics Series. Mineola, NY: Dover Publications.
Knill, E. and Laflamme, R. 1997. Theory of quantum error-correcting codes. Phys. Rev. A, 55(Feb), 900–911.
Kretschmann, D. and Werner, R. F. 2005. Quantum channels with memory. Phys. Rev. A, 72, 062323.
Leung, D. 2001. Towards Robust Quantum Computation PhD thesis, Stanford University. Ljys, 48, 199.
Lindblad, G. 1999. A general no-cloning theorem. Lett. Math. Phys., 47(2), 189–196.
Lo, H.-K. and Chau, H. F. 1997. Is quantum bit commitment really possible? Phys. Rev. Lett., 78, 3410.
Ludwig, G. 1983. Foundations of Quantum Mechanics. New York, NY: Springer-Verlag.
Mac Lane, S. 1978. Categories for the Working Mathematician, Vol. 5. Berlin: Springer Science & Business Media.
Mackey, G. W. 1963. The Mathematical Foundations of Quantum Mechanics, Vol. 1. Mineola, NY: Dover Publications.
Masanes, L. and Müller, M. P. 2011. A derivation of quantum theory from physical requirements. New J. Phys., 13(6), 063001.
Masanes, L., Müller, M. P, Augusiak, R., and Pérez-Garćıa, D. 2013. Existence of an information unit as a postulate of quantum theory. Proc. Nat. Acad. Sci., 110(41), 16373–16377.
Mayers, D. 1997. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett., 78, 3414.
Nielsen, M. A. and Chuang, I. L. 1997. Programmable quantum gate arrays. Phys. Rev. Lett., 79(2), 321–324.
Oreshkov, O., Costa, F., and Brukner, C. 2012. Quantum correlations with no causal order. Nature Commun., 3, 1092.
Ozawa, M. 1984. Quantum measuring processes of continuous observables. J. Math. Phys., 25, 79.
Ozawa, M. 1997. Quantum state reduction and the quantum bayes principle. Pages 233– 241 of: Hirota, O., Holevo, A. S., and Caves, C. M. (eds), Quantum Communication, Computing and Measurement. New York, NY: Plenum.
Paris, M. and Rehacek, J. 2004. Quantum State Estimation, Vol. 649. Berlin: Springer.
Parthasarathy, K. R. 1999. Extremal decision rules in quantum hypothesis testing. Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 02(04), 557–568.
Paulsen, V. I. 1986. Completely Bounded Maps and Dilations. Harlow, UK: Longman Scientific and Technical.
Pearl, J. 2012. Causality: Models, Reasoning, and Inference. Cambridge: Cambridge University Press.
Penrose, R. 1971. Applications of negative dimensional tensors. Pages 221–244 of: Welsh, D. J. A. (ed.), Combinatorial Mathematics and its Applications. New York, NY: Academic Press.
Piron, C. 1964. Axiomatique quantique. Helvetica Phys. Acta, 37(4-5), 439.
Piron, C. 1976. Foundations of Quantum Physics. Mathematical Physics Monograph Series. Benjamin-Cummings Publishing Company.
Planck, M. 1941. Der Kausalbegriff in der Physik. Verlag von S. Hirzel.
Plenio, M. B. and Virmani, S. 2007. An introduction to entanglement measures. Quantum Inf. Comput., 7, 1.
Procopio, L. M, Moqanaki, A., Araújo, M., Costa, F., Alonso Calafell, I., Dowd, E. G., et al. 2015. Experimental superposition of orders of quantum gates. Nature Commun., 6(Aug.), 7913.
Rambo, T., Altepeter, J., D'Ariano, G. M., and Kumar, P. 2012. Functional quantum computing: an optical approach. arXiv:1211.1257.
Rockafellar, R. T. 2015. Convex Analysis. Princeton, NJ: Princeton University Press.
Royer, A. 1994. Reversible quantum measurements on a spin 1/2 and measuring the state of a single system. Phys. Rev. Lett., 73, 913–917.
Royer, A. 1995. Reversible quantum measurements on a spin 1/2 and measuring the state of a single system (erratum). Phys. Rev. Lett., 74, 1040–1040.
Russel, B. 1912. On the notion of cause. Proc. Aristotelian Soc., 13, 1–26.
Salmon, W. 1967. The Foundations Of Scientific Inference. Pittsburgh, PA: University of Pittsburgh Press.
Salmon, W. C. 1998. Causality and Explanation: Wesley C. Salmon. Oxford Scholarship online. Oxford University Press.
Schrödinger, E. 1935a. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften, 23, 807–812; 823–828; 844–849.
Schrödinger, E. 1935b. Probability relations between separated systems. Pages 555–563 of: Proc. Camb. Phil. Soc, vol. 31. Cambridge Univ Press.
Schumacher, B. 1996. Sending entanglement through noisy quantum channels. Phys. Rev. A, 54, 2614–2628.
Schumacher, B. and Nielsen, M. A. 1996. Quantum data processing and error correction. Phys. Rev. A, 54, 2629–2635.
Schumacher, B. and Westmoreland, M. D. 2012. Modal quantum theory. Found. Phys., 42(7), 918–925.
Scott, A. J. and Grassl, M. 2009. SIC-POVMs: a new computer study. arXiv preprint arXiv:0910.5784.
Selinger, P. A Survey of Graphical Languages for Monoidal Categories. Available at
Selinger, P. 2011. A survey of graphical languages for monoidal categories. Pages 289–355 of: New Structures for Physics. Berlin: Springer.
Shor, P. W. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comp., 26(5), 1484–1509.
Smithey, D. T., Beck, M., Raymer, M. G., and Faridani, A. 1993. Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum. Phys. Rev. Lett., 70(Mar), 1244–1247.
Solovay, R. M. 1970. A model of set theory in which every set of reals is Lebesgue measurable. Annals of Mathematics, 92, 1–56.
Ueda, M. and Kitagawa, M. 1992. Reversibility in quantum measurement processes. Phys.Rev. Lett., 68, 3424–3427.
Uhlmann, A. 1977. Relative entropy and the Wigner–Yanase–Dyson–Lieb concavity in an interpolation theory. Commun. Math. Phys., 54(1), 21–32.
Varadarajan, V. S. 1962. Probability in physics and a theorem on simultaneous observability. Comm. Pure Appl. Math., 15, 189.
Vogel, K. and Risken, H. 1989. Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. Phys. Rev. A, 40(Sep), 2847–2849.
von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer-Verlag. Translated as Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955. Chap. 4.
von Neumann, J. 1996. Mathematical Foundations of Quantum Mechanics, Vol. 2. Princeton, NJ: Princeton university press.
Werner, R. F. 1989. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40, 4277–4281.
Wheeler, J. A. 1990. Complexity, entropy and the physics of information. In: Zurek, W. H. (ed.), Santa Fe Institute Studies in the Sciences of Complexity, Proceedings of the 1988 Workshop on Complexity, Entropy and the Physics of Information, Santa Fe, New Mexico, May–June, 1989. Redwood City, CA: Addison-Wesley.
Wiesner, S. 1983. Conjugate coding. Sigact News, 15, 78.
Wilce, A. 2010. Formalism and interpretation in quantum theory. Foundations of Physics, 40(4), 434–462.
Wilce, A. 2012. Conjugates, correlation and quantum mechanics. arXiv:1206.2897.
Wootters, W. K. and Zurek, W. H. 1982. A single quantum cannot be cloned. Nature, 299(5886), 802–803.
Yao, A. C.-C. 1993. Quantum circuit complexity. Pages 352–361 of: Proceedings of Thirty-fourth IEEE Symposium on Foundations of Computer Science (FOCS1993).
Yuen, H. P. 1986. Amplification of quantum states and noiseless photon amplifiers. Phys. Lett. A, 113, 405–407.
Yuen, H. P. 2012. An unconditionally secure quantum bit commitment protocol. arXiv preprint arXiv:arXiv:1212.0938v1.


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