Research interests

For an overview, please see the pages of my research group at IQOQI Vienna.
Citation statistics: Google Scholar.

Media coverage

  • Our results on the Berry-Keating conjecture (paper 43) have been greatly exaggerated by some media (e.g. the Wire), which in turn has led to criticism (e.g. here). To clarify: no, our work will almost certainly not lead to significant progress on the Riemann conjecture! But we think it is an interesting insight, and its main observation is fully mathematically rigorous. See also Nature Physics, the Reference Frame,, Quanta magazine, Spektrum der Wissenschaft.

  • Quantum perspective. New Scientist, February 5, 2022. Describes our result (publication 40) on deriving the Lorentz transformations from properties of quantum communication, and how they have inspired recent work by Flavio Mercati and Giovanni Amelino-Camelia.

  • Why space has exactly three dimensions. New Scientist, September 25, 2013. Discusses some approaches towards this question, including our publication 32 below.
  • Quantum causality: information insights. Nature Physics 8, 860 (2012). Article by Terry Rudolph on recent work by the quantum foundations community, including our work on the structure of space and quantum theory (publications 29 and 32).


Preprints on arXiv

  1. C. L. Jones and M. P. Müller, Thinking twice inside the box: is Wigner's friend really quantum?, arXiv:2402.08727
  2. A. Aloy, T. D. Galley, C. L. Jones, S. L. Ludescher, and M. P. Müller, Spin-bounded correlations: rotation boxes within and beyond quantum theory, arXiv:2312.09278
  3. K. J. McQueen, I. T. Durham, and M. P. Müller, Building a quantum superposition of conscious states with integrated information theory, arXiv:2309.13826
  4. Ll. Masanes, T. D. Galley, and M. P. Müller, Response to "The measurement postulates of quantum mechanics are not redundant", arXiv:2309.01650
  5. C. L. Jones, S. L. Ludescher, A. Aloy, and M. P. Müller, Theory-independent randomness generation with spacetime symmetries, arXiv:2210.14811
  6. A. de la Hamette, T. D. Galley, P. A. Höhn, L. Loveridge, and M. P. Müller, Perspective-neutral approach to quantum frame covariance for general symmetry groups, arXiv:2110.13824


Peer-reviewed publications

  1. M. P. Müller and A. J. P. Garner, Testing Quantum Theory by Generalizing Noncontextuality, Phys. Rev. X 13, 041001 (2023), arXiv:2112.09719
  2. M. Krumm and M. P. Müller, Free Agency and Determinism: Is There a Sensible Definition of Computational Sourcehood?, Entropy 25(6), 903 (2023), arXiv:2101.12033
  3. A. de la Hamette, S. L. Ludescher, and M. P. Müller, Entanglement-asymmetry correspondence for internal quantum reference frames, Phys. Rev. Lett. 129, 260404 (2022), arXiv:2112.00046
  4. P. A. Höhn, M. Krumm, and M. P. Müller, Internal quantum reference frames for finite Abelian groups, J. Math. Phys. 63, 112207 (2022), arXiv:2107.07545
  5. R. D. Baldijão, M. Krumm, A. J. P. Garner, and M. P. Müller, Quantum Darwinism and the spreading of classical information in non-classical theories, Quantum 6, 636 (2022), arXiv:2012.06559
  6. M. Krumm, P. A. Höhn, and M. P. Müller, Quantum reference frame transformations as symmetries and the paradox of the third particle, Quantum 5, 530 (2021), arXiv:2011.01951
  7. G. Chiribella, A. Cabello, M. Kleinmann, and M. P. Müller, General Bayesian theories and the emergence of the exclusivity principle, Phys. Rev. Research 2, 042001(R) (2020), arXiv:1901.11412
  8. M. P. Müller, Law without law: from observer states to physics via algorithmic information theory, Quantum 4, 301 (2020), arXiv:1712.01826
  9. A. J. P. Garner, M. Krumm, and M. P. Müller, Semi-device-independent information processing with spatiotemporal degrees of freedom, Phys. Rev. Research 2, 013112 (2020), arXiv:1907.09274
  10. M. Lostaglio and M. P. Müller, Coherence and asymmetry cannot be broadcast, Phys. Rev. Lett. 123, 020403 (2019), arXiv:1812.08214
  11. Ll. Masanes, T. D. Galley, and M. P. Müller, The measurement postulates of quantum mechanics are operationally redundant, Nat. Comm. 10, 1361 (2019), arXiv:1811.11060
  12. P. Boes, J. Eisert, R. Gallego, M. P. Müller, and H. Wilming, Von Neumann entropy from unitarity, Phys. Rev. Lett. 122, 210402 (2019), arXiv:1807.08773
  13. M. Krumm and M. P. Müller, Quantum computation is the unique reversible circuit model for which bits are balls, npj Quantum Inf. 5, 7 (2019), arXiv:1804.05736
  14. J. Riddell and M. P. Müller, Generalized eigenstate typicality in translation-invariant quasifree fermionic models, Phys. Rev. B 97, 035129 (2018), arXiv:1709.05569
  15. M. P. Müller, Correlating thermal machines and the second law at the nanoscale, Phys. Rev. X 8, 041051 (2018), arXiv:1707.03451
  16. J. Scharlau and M. P. Müller, Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics, Quantum 2, 54 (2018), arXiv:1605.06092
  17. M. P. Müller, S. Carrozza, and P. A. Höhn, Is the local linearity of space-time inherited from the linearity of probabilities?, J. Phys. A: Math. Theor. 50, 054003 (2017), arXiv:1608.08684
  18. M. Krumm, H. Barnum, J. Barrett, and M. P. Müller, Thermodynamics and the structure of quantum theory, New J. Phys. 19, 043025 (2017), arXiv:1608.04461
  19. C. M. Bender, D. C. Brody, and M. P. Müller, Hamiltonian for the zeros of the Riemann zeta function, Phys. Rev. Lett. 118, 130201 (2017), arXiv:1608.03679. PRL: Editor's Suggestion.
  20. A. J. P. Garner, M. P. Müller, and O. C. O. Dahlsten, The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer, Proc. R. Soc. A 473, 20170596 (2017), arXiv:1412.7112
  21. M. P. Müller and M. Pastena, A generalization of majorization that characterizes Shannon entropy, IEEE Trans. Inf. Th. 62(4), 1711-1720 (2016), arXiv:1507.06900
  22. P. A. Höhn and M. P. Müller, An operational approach to spacetime symmetries: Lorentz transformations from quantum communication, New J. Phys. 18, 063026 (2016),  arXiv:1412.8462. In NJP's "Highlights of 2016" collection.
  23. M. Lostaglio, M. P. Müller, and M. Pastena, Stochastic independence as a resource in small-scale thermodynamics, Phys. Rev. Lett. 115, 150402 (2015), arXiv:1409.3258. PRL: Editor's Suggestion.
  24. M. P. Müller, E. Adlam, Ll. Masanes, and N. Wiebe, Thermalization and canonical typicality in translation-invariant quantum lattice systems, Commun. Math. Phys. 340(2), 499-561 (2015), arXiv:1312.7420
  25. G. Gour, M. P. Müller, V. Narasimhachar, R. W. Spekkens, and N. Yunger Halpern, The resource theory of informational nonequilibrium in thermodynamics, Phys. Rep. 583, 1-58 (2015), arXiv:1309.6586
  26. H. Barnum, J. Barrett, M. Krumm, and M. P. Müller, Entropy, majorization and thermodynamics in general probabilistic theories, Electronic Proceedings in Theoretical Computer Science 195, 43-58 (2015), arXiv:1508.03107
  27. H. Barnum, M. P. Müller, and C. Ududec, Higher-order interference and single-system postulates characterizing quantum theory, New J. Phys. 16, 123029 (2014), arXiv:1403.4147
  28. Ll. Masanes, M. P. Müller, D. Pérez-García, and R. Augusiak, Entanglement and the three-dimensionality of the Bloch ball, J. Math. Phys. 55, 122203 (2014), arXiv:1111.4060
  29. Ll. Masanes, M. P. Müller, R. Augusiak, and D. Pérez-García, Existence of an information unit as a postulate of quantum theory, Proc. Natl. Acad. Sci. USA 110(41), 16373 (2013), arXiv:1208.0493
  30. M. P. Müller and Ll. Masanes, Three-dimensionality of space and the quantum bit: an information-theoretic approach, New J. Phys. 15, 053040 (2013), arXiv:1206.0630.
    In NJP's "Highlights of 2013" collection.
  31. M. P. Müller, J. Oppenheim, and O. C. O. Dahlsten, The black hole information problem beyond quantum theory, J. High Energy Phys. 09, 116 (2012), arXiv:1206.5030
  32. J. Eisert, M. P. Müller, and C. Gogolin, Quantum measurement occurrence is undecidable, Phys. Rev. Lett. 108, 260501 (2012), arXiv:1111.3965
  33. G. de la Torre, Ll. Masanes, A. J. Short, and M. P. Müller, Deriving quantum theory from its local structure and reversibility, Phys. Rev. Lett. 109, 090403 (2012), arXiv:1110.5482
  34. M. P. Müller and C. Ududec, Structure of reversible computation determines the self-duality of quantum theory, Phys. Rev. Lett. 108, 130401 (2012), arXiv:1110.3516
  35. M. P. Müller, O. C. O. Dahlsten, and V. Vedral, Unifying typical entanglement and coin tossing: on randomization in probabilistic theories, Commun. Math. Phys. 316(2), 441-487 (2012), arXiv:1107.6029
  36. C. Gogolin, M. P. Müller, and J. Eisert, Absence of thermalization in non-integrable systems, Phys. Rev. Lett. 106, 040401 (2011), arXiv:1009.2493
  37. Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011), arXiv:1004.1483
  38. M. P. Müller, D. Gross, and J. Eisert, Concentration of measure for quantum states with a fixed expectation value, Commun. Math. Phys. 303(3), 785-824 (2011), arXiv:1003.4982
  39. M. Müller and D. Schleicher, How to add a noninteger number of terms: from axioms to new identities, Am. Math. Mon. 118(2), 136-152 (2011), arXiv:1001.4695
  40. N. Ay, M. Müller, and A. Szkola, Effective complexity of stationary process realizations, Entropy 13 (6), 1200-1211 (2011), arXiv:1001.2686
  41. D. Gross, M. Müller, R. Colbeck, and O. C. O. Dahlsten, All reversible dynamics in maximally non-local theories are trivial, Phys. Rev. Lett. 104, 080402 (2010), arXiv:0910.1840
  42. N. Ay, M. Müller, and A. Szkola, Effective complexity and its relation to logical depth, IEEE Trans. Inf. Th. 56(9), 4593-4607 (2010), arXiv:0810.5663
  43. M. Müller, Stationary algorithmic probability, Theor. Comput. Sci. 411, 113-130 (2010), arXiv:cs.IT/0608095
  44. M. Müller and D. Schleicher, Fractional sums and Euler-like identities, Ramanujan J. 21(2), 123-143 (2010), arXiv:math/0502109
  45. M. Müller, Convex trace functions on quantum channels and the additivity conjecture, Phys. Rev. A 79, 052332 (2009), arXiv:0809.4060
  46. M. Müller, C. Rogers, and R. Nagarajan, Lossless quantum prefix compression for communication channels that are always open, Phys. Rev. A 79, 012302 (2009), arXiv:0808.2003
  47. M. Müller, Does probability become fuzzy in small regions of spacetime?, Phys. Lett. B 673, 166-167 (2009), arXiv:0712.4090
  48. M. Müller, On the quantum Kolmogorov complexity of classical strings, Int. J. Quant. Inf. 7 (4), 701-711 (2009), arXiv:0707.2924
  49. M. Müller, Strongly universal quantum Turing machines and invariance of Kolmogorov complexity, IEEE Trans. Inf. Th. 54(2), 763--780 (2008), arXiv:quant-ph/0605030
  50. F. Benatti, T. Krüger, M. Müller, Ra. Siegmund-Schultze, and A. Szkola, Entropy and quantum Kolmogorov complexity: a quantum Brudno's theorem, Commun. Math. Phys. 265(2), 437-461 (2006), arXiv:quant-ph/0506080
  51. M. Müller and D. Schleicher, How to add a non-integer number of terms, and how to produce unusual infinite summations, J. Comp. Appl. Math. 178 (1-2), 347-360 (2005), download


All further publications

  1. T. D. Galley, Ll. Masanes, and M. P. Müller, Reply to "Masanes-Galley-Müller and the State-Update Postulate", arXiv:2212.03629
  2. M. P. Müller, Undecidability and unpredictability: not limitations, but triumphs of science, in A. Aguirre, Z. Merali, and D. Sloan (eds.), "Undecidability, Uncomputability, and Unpredictability", Springer Nature, 2021, arXiv:2008.09821. First prize at the 2021 FQXi essay contest.
  3. M. P. Müller, Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes), SciPost Phys. Lect. Notes 28 (2021), arXiv:2011.01286
  4. A. J. P. Garner and M. P. Müller, Characterization of the probabilistic models that can be embedded in quantum theory, arXiv:2004.06136. Contains a condensed version of Theorem 2 of (and is superseded by) arXiv:2112.09719.
  5. M. P. Müller, Mind before matter: reversing the arrow of fundamentality, in A. Aguirre, B. Foster, and Z. Merali (eds.), What is Fundamental?, Springer Verlag, 2019, arXiv:1812.08594
  6. P. A. Höhn, M. P. Müller, C. Pfeifer, and D. Rätzel, A local quantum Mach principle and the metricity of spacetime, arXiv:1811.02555
  7. A. Koberinski and M. P. Müller, Quantum theory as a principle theory: insights from an information-theoretic reconstruction, in M. E. Cuffaro and S. C. Fletcher (eds.), Physical Perspectives on Computation, Computational Perspectives on Physics, Cambridge University Press, Cambridge, 2018, arXiv:1707.05602
  8. C. M. Bender, D. C. Brody, and M. P. Müller, Comment on 'Comment on "Hamiltonian for the zeros of the Riemann zeta function' ", arXiv:1705.06767
  9. M. P. Müller, A note on "Hamiltonian for the zeros of the Riemann zeta function", arXiv:1704.04705
  10. M. P. Müller, J. Oppenheim, and O. C. O. Dahlsten, Hiding information in theories beyond quantum mechanics, and its application to the black hole information problem, Horizons of Quantum Physics Conference Proceedings, Foundations of Physics, Springer, 2014.
  11. M. P. Müller and Ll. Masanes, Information-theoretic postulates for quantum theory, in "Quantum Theory: Informational Foundations and Foils", G. Chiribella and R. W. Spekkens (editors), Springer, 2016, arXiv:1203.4516
  12. M. Müller and C. Rogers, Quantum bit strings and prefix-free Hilbert spaces, ITSL '08 conference proceedings, arXiv:0804.0022



  • PhD thesis: Quantum Kolmogorov complexity and the quantum Turing machine (2007), arXiv:0712.4377. Supervised by Prof. Ruedi Seiler, Institut für Mathematik, Technische Universität Berlin. Grade: with distinction (summa cum laude).
  • Diploma thesis: Das Quanten-Shannon-Mc-Millan-Breiman-Theorem am Beispiel der Heisenbergschen Spinkette (2004). Grade: very good.


Science writing by myself (about work by others)


Early research before university

  • Experimental disproof of an alleged antigravity experiment ("Schnurer's experiment"), with Josip Milanovic and Franz-Josef Schmitt (1999).
    At that time, a popular German TV broadcast claimed that a superconductor could yield an antigravity effect in a simple experiment. Thus, we went to the lab at University Erlangen and reproduced the experiment. We found that Schnurer seems to have misinterpreted a simple buoyancy effect.
  • "Fractional sums": how to add a non-integer number of terms (around 1998).
    This idea led to several publications with Dierk Schleicher (for example this one), and made the first prize at the German youth science fair "Jugend forscht" 1998 in mathematics and computer science, together with an exceptional prize by the Federal President.
  • Higher-order arithmetic operations, and non-integer iteration of functions (1994-1995).
    The main idea is written up in a little document here. It made the second prize at "Jugend forscht", and an exceptional prize by the Federal Chancellor.