Some Negative Remarks on Operational Approaches to Quantum Theory

Part of the Fundamental Theories of Physics book series (FTPH, volume 181)


Over the last 10 years there has been an explosion of “operational reconstructions” of quantum theory. This is great stuff: For, through it, we come to see the myriad ways in which the quantum formalism can be chopped into primitives and, through clever toil, brought back together to form a smooth whole. An image of an IQ-Block puzzle comes to mind, There is no doubt that this is invaluable work, particularly for our understanding of the intricate connections between so many quantum information protocols. But to me, it seems to miss the mark for an ultimate understanding of quantum theory; I am left hungry. I still want to know what strange property of matter forces this formalism upon our information accounting. To play on something Einstein once wrote to Max Born, “The quantum reconstructions are certainly imposing. But an inner voice tells me that they are not yet the real thing. The reconstructions say a lot, but do not really bring us any closer to the secret of the ‘old one’.” In this talk, I hope to expand on these points and convey some sense of why I am fascinated with the problem of the symmetric informationally complete POVMs to an extent greater than axiomatic reconstructions.


  1. 1.
    C.A. Fuchs, A. Peres, Quantum theory needs no ‘interpretation’. Phys. Today 53(3), 70 (2000)CrossRefGoogle Scholar
  2. 2.
    C.A. Fuchs, Coming of Age with Quantum Information (Cambridge University Press, Cambridge, 2010)Google Scholar
  3. 3.
    C.A. Fuchs, Quantum mechanics as quantum information (and only a little more) (2002). arXiv:quant-ph/0205039v1. Abridged version, in Quantum Theory: Reconsideration of Foundations, ed. by A. Khrennikov (Växjö University Press, Växjö, 2002), pp. 463–543
  4. 4.
    G. Chiribella, G.M. D’Ariano, P. Perinotti, Informational derivation of quantum theory. Phys. Rev. A 84, 012311 (2011). arXiv:1011.6451
  5. 5.
    Č. Brukner, Questioning the rules of the game. Physics 4, 55 (2011)CrossRefGoogle Scholar
  6. 6.
    B. Dakić, Č. Brukner, Quantum theory and beyond: is entanglement special?, in Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, ed. by H. Halvorson (Cambridge University Press, Cambridge, 2011), pp. 365–392. arXiv:0911.0695
  7. 7.
    L. Hardy, Quantum theory from five reasonable axioms (2001). arXiv:quant-ph/0101012v4
  8. 8.
    R. Schack, Quantum theory from four of Hardy’s axioms. Found. Phys. 33, 1461 (2003). arXiv:quant-ph/0210017
  9. 9.
    L. Hardy, Reformulating and reconstructing quantum theory (2011). arXiv:1104.2066
  10. 10.
    M.P. Müller, L. Masanes, Information-theoretic postulates for quantum theory (2012). arXiv:1203.4516
  11. 11.
    A. Wilce, Four and a half axioms for finite dimensional quantum mechanics (2009). arXiv:0912.5530
  12. 12.
    A. Einstein, Quantenmechanik und Wirklichkeit. Dialectica 2, 320–24 (1948). The English translation used here is from D. Howard, Einstein on Locality and Separability, Stud. Hist. Phil. Sci. Part A 16, 171–201 (1985). Another translation can be found in The Born–Einstein Letters, ed. by M. Born (Macmillan, 1971), p. 170Google Scholar
  13. 13.
    A. Peres, Unperformed experiments have no results. Am. J. Phys. 46, 745 (1978)ADSCrossRefGoogle Scholar
  14. 14.
    J. Conway, S. Kochen, The Free Will Theorem. Found. Phys. 36, 1441–73 (2006). arXiv:quant-ph/0604079
  15. 15.
    C.M. Caves, C.A. Fuchs, R. Schack, Subjective probability and quantum certainty, Stud. Hist. Phil. Mod. Phys. 38, 255–274 (2007). arXiv:quant-ph/0608190
  16. 16.
    A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)ADSCrossRefMATHGoogle Scholar
  17. 17.
    A. Peres, Two simple proofs of the Kochen-Specker theorem. J. Phys. A 24, L175 (1991)ADSMathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    A. Peres, Quantum Theory: Concepts and Methods, Chapter 7 (Kluwer, Dordrecht, 1993)Google Scholar
  19. 19.
    A. Peres, Generalized Kochen–Specker theorem. Found. Phys. 26, 807–12 (1996), arXiv:quant-ph/9510018
  20. 20.
    C.A. Fuchs, R. Schack, A quantum-Bayesian route to quantum-state space. Found. Phys. 41, 345–356 (2011). arXiv:0912.4252
  21. 21.
    D.M. Appleby, Å. Ericsson, C.A. Fuchs, Properties of QBist state spaces. Found. Phys. 41, 564–579 (2011). arXiv:0910.2750
  22. 22.
    C.A. Fuchs, R. Schack, Quantum-Bayesian coherence. Rev. Mod. Phys. 85, 1693–1715 (2013). arXiv:1301.3274
  23. 23.
    G. Zauner, Quantum designs—foundations of a noncommutative theory of designs. Ph.D. thesis, University of Vienna (1999).
  24. 24.
    J.M. Renes, R. Blume-Kohout, A.J. Scott, C.M. Caves, Symmetric informationally complete quantum measurements. J. Math. Phys. 45(6), 2171 (2004). arXiv:quant-ph/0310075
  25. 25.
    I. Bengtsson, K. Blanchfield, A. Cabello, A Kochen–Specker inequality from a SIC. Phys. Lett. A 376, 374–76 (2010). arXiv:quant-ph/1109.6514
  26. 26.
    A.J. Scott, M. Grassl, SIC-POVMs: A new computer study. J. Math. Phys. 51, 042203 (2010). arXiv:quant-ph/0910.5784
  27. 27.
    D.M. Appleby, S.T. Flammia, C.A. Fuchs, The Lie algebraic significance of symmetric informationally complete measurements. J. Math. Phys. 52, 02202 (2011). arXiv:quant-ph/1001.0004
  28. 28.
    J.I. Rosado, Representation of quantum states as points in a probability simplex associated to a SIC-POVM. Found. Phys. 41 1200–13 (2011). arXiv:quant-ph/1007.0715
  29. 29.
    G.N.M. Tabia, Experimental scheme for qubit and qutrit SIC-POVMs using multiport devices. Phys. Rev. A 86, 062107 (2012). arXiv:quant-ph/1207.6035
  30. 30.
    G.N.M. Tabia, D.M. Appleby, Exploring the geometry of qutrit state space using symmetric informationally complete probabilities. Phys. Rev. A 88, 012131 (2013). arXiv:quant-ph/1304.8075
  31. 31.
    D.M. Appleby, C.A. Fuchs, H. Zhu, Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem (2013). arXiv:quant-ph/1312.0555
  32. 32.
    J.A. Wheeler, The quantum and the universe, in Relativity, Quanta and Cosmology, vol. 2, ed. by M. Pantaleo, F. de Finis (Johnson Reprint Corp., New York, 1979)Google Scholar
  33. 33.
    N.D. Mermin, What’s wrong with this pillow?. Phys. Today 42(4), 9, 11 (1989)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Raytheon BBN TechnologiesCambridgeUSA
  2. 2.Martin A. Fisher School of PhysicsBrandeis UniversityWalthamUSA

Personalised recommendations