Publications and Preprints

(Links are to .pdf files of preprints. An asterisk indicates a student co-author.)


  1. Composites and categories of Euclidean Jordan algebras (with H. Barnum and M. Graydon), 2016
  2. Conjugates, filters and quantum mechanics, 2012 (revised 2015)
  3. Symmetry, self-duality and the Jordan structure of quantum mechanics, 2011
  4. Ordered linear spaces and categories as frameworks for information-processing characterizations of quantum and classical Theory (with H. Barnum), 2009
  5. Cloning and broadcasting in generic probabilistic theories  (with Howard Barnum, Jon Barrett and Matt Leifer), 2006 (awaiting eventual revision)
  6. Influence-free states on compound quantum systems  (with Howard Barnum, Chris Fuchs and Joe Renes), 2005 (awaiting eventual revision)



  1. A royal road to quantum mechanics (or thereabouts), Entropy 20 (2018)
  2. A shortcut from categorical quantum mechanics to convex operational theories, in B. Coecke and A. Kissinger, Proceedings of the 14th International Conference on Quantum Theory and Logic, EPTCS 266, 2018
  3. A royal road to quantum mechanics (or thereabouts), extended abstract, in  R. Duncan and C. Huenen, eds., Proceedings of the 13th International Conference on Quantum Theory and Logic, EPTCS 236 (2017)
  4. Post-classical probability theory (with Howard Barnum), invited chapter in Quantum Theory: Informational Foundations and Foils, G. Chiribella and R. Spekkens, eds., Springer, 2016
  5. Some nearly quantum theories (with Howard Barnum and Matthew Graydon), EPTCS 195 (2015)
  6. Local Tomography and the Jordan structure of Quantum Theory (with Howard Barnum), Foundations of Physics 44 (2014)
  7. Ensemble Steering. Weak Self-Duality and the Structure of Probabilistic Theories (with Howard Barnum and Philipp Gaebler*) Foundations of Physics 43 (2013)
  8. Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models (with Howard Barnum and Ross Duncan), 2009, Proceedings of the workshop Quantum Logic Inspired by Quantum Communication, Indiana University, May 2009, (J. M. Dunn and L. Moss, eds.),  J. Phil. Logic 42, 2013
  9. Symmetry and Self-Duality in Categories of Probabilistic Models”,  EPTCS 95 (2012), 275-279
  10. Teleportation in Generalized Probabilistic Theories (with Howard Barnum, Jon Barrett and Matt Leifer), in S. Abramsky and M. Mislove, eds., Mathematical Foundations of Information Flow, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, 2012
  11. Four and a Half Axioms for Finite-Dimensional Quantum Mechanics, in M. Hemmo and Y. Ben-Menahem (eds.),  Probability in Physics: essays in honor of Itamar Pitowsky, Springer, 2012
  12. Symmetry and composition in Generalized Probabilistic Theories, Proceedings of QLP VI, in Electronic Lecture Notes in Theoretical Computer Science 270, Issue 2,  (2011),  191-207
  13. Information Processing in Convex Operational Theories (with Howard Barnum), Electronic Notes in Theoretical Computer Science 270, Issue 1 (2011), 3-15

14.   Entropy and Information Causality in Generalized Probabilistic Theories (with H. Barnum, J. Barrett, L. Clark, M. Leifer, R. Spekkens, N. Stepanik*, and R. Wilke*), New Journal of Physics 12 (2010), 1367-2630; addendum, New J. Physics 14 (2012), p. 129401. Addendum, New J. Physics 14 (2012), p. 129401

  1. Formalism and Interpretation in Quantum Theory (invited paper for a Festschrift in honor of Jeff Bub’s 65th birthday),  Foundations of Physics, 40 (2010) , 434-462
  2. Test Spaces, 120+ pp, commissioned chapter for the Handbook of Quantum Logic, vol. II, D. Gabbay, K. Engesser and D. Lehman, eds., Elsevier (2008)
  3. Covariance in Quantum Logic (with Q. Tran*) International Journal of Theoretical  Physics 47 (2008), 15-25
  4. A Generic No-Broadcasting Theorem (with Howard Barnum, Jon Barrett and Matt Leifer),   Physical Review Letters 77 (2007)
  5. Review of Quantum Entanglements: selected papers of Rob Clifton, edited by Jeremy Butterfield and Hans Halvorson, Oxford University Press, 2004.  Philosophy of Science 73 (2006), 122-124
  6. Symmetry and Topology in Quantum Logic,  International Journal of Theoretical Physics 44 (2005) 2303-2316
  7. Compact Orthoalgebras, Proceedings of the American Mathematical Society 133 (2005), 2911-2920. (An older version, Topological Orthoalgebras, contains additional material -- plus typos and other infelicities.)
  8. Topological Test Spaces,   International Journal of Theoretical Physics 44 (2005), 1227-1238
  9. Compactness and Symmetry in Quantum Logic Proceedings of the conference Quantum Theory: Reconsideration of Foundations 2 (International Center for Mathematical Modeling, Växjo University, Växjo, Sweden, June 2003), A. Khrennikov, ed., Växjo University Press, 2004.
  10. Degenerate Fibres in the Stone-Cech Compactification of the Universal Bundle of a Finite Group (with D. V. Feldman), Transactions of the American Mathematical Society 354 (2002), 3757-3769.
  11. Quantum Logic and Quantum Probability, commissioned article for the Stanford Encyclopedia of Philosophy,  Feb. 2002; revised February, 2006 and August 2012
  12. On generalized Sasaki Projections, Int. J. Theor. Phys. 39 (2000), 969-974
  13. Current Research in Operational Quantum Logic (Ed., with B. Coecke and D. J. Moore), Kluwer, 2000. Contributed three chapters:
  14. Operational quantum logic: an overview (with B. Coecke and D. J. Moore), pp. 1-36 of [23] (A slightly different version can be found here.)
  15. Test Spaces and Orthoalgebras, pp. 81-114 of [23]. (Largely superseded by [8])
  16. Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics (with D. J. Foulis), pp. 139-165 of [23]
  17. Superentangled States (with R. Clifton, D. V. Feldman, H. Halvorson and M. Redhead), Physical Review A 58 (1998), 135-145. (Here is an earlier version .)
  18. Abelian Extensions of Quantum Logics (with D. V. Feldman), International Journal of Theoretical Physics 37 (1998), 39-42
  19. Perspectivity and Congruence in Partial Abelian Semigroups, Mathematica Slovaca 48 (1998), 112-135
  20. Symmetric Test Spaces, in S. Hotaling and S. Pirich (Eds.), Photonic Quantum Computing, Proceedings of the SPIEE 3067 (1997) 116-129
  21. Pull-backs and Product Tests, Helvetica Physica Acta 70 (1997), 803-812
  22. Representations of D-Posets (with S. Pulmannová), International Journal of Theoretical Physics 34 (1995), 1689-1696
  23. Partial Abelian Semigroups, International Journal of Theoretical Physics 34 (1995), 1807-1812
  24. Sigma-Additivity in Manuals and Orthoalgebras (with D. V. Feldman), Order 10 (1993), 383-392
  25. Tensor Products in Generalized Measure Theory, International Journal of Theoretical Physics 31 (1992), 1915-1928
  26. The Tensor Product of Frame Manuals, International Journal of Theoretical Physics 29 (1990) 805-814 
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