Research interests

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

Media coverage

  • 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. M. P. Müller and A. J. P. Garner, Testing quantum theory with generalized noncontextuality, arXiv:2112.09719
  2. A. de la Hamette, S. L. Ludescher, and M. P. Müller, Entanglement/Asymmetry correspondence for internal quantum reference frames, arXiv:2112.00046
  3. 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
  4. P. A. Höhn, M. Krumm, and M. P. Müller, Internal quantum reference frames for finite Abelian groups, arXiv:2107.07545
  5. M. Krumm and M. P. Müller, Computational irreducibility and compatibilism: towards a formalization, arXiv:2101.12033
  6. 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, arXiv:2012.06559
  7. P. A. Höhn, M. P. Müller, C. Pfeifer, and D. Rätzel, A local quantum Mach principle and the metricity of spacetime, arXiv:1811.02555


Publications in peer-reviewed journals

  1. 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
  2. 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
  3. M. P. Müller, Law without law: from observer states to physics via algorithmic information theory, Quantum 4, 301 (2020), arXiv:1712.01826
  4. 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
  5. M. Lostaglio and M. P. Müller, Coherence and asymmetry cannot be broadcast, Phys. Rev. Lett. 123, 020403 (2019), arXiv:1812.08214
  6. 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
  7. 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
  8. M. Krumm and M. P. Müller, Quantum computation is the unique reversible circuit model for which bits are balls, npj Quantum Information 5, 7 (2019), arXiv:1804.05736
  9. J. Riddell and M. P. Müller, Generalized eigenstate typicality in translation-invariant quasifree fermionic models, Phys. Rev. B 97, 035129 (2018), arXiv:1709.05569
  10. M. P. Müller, Correlating thermal machines and the second law at the nanoscale, Phys. Rev. X 8, 041051 (2018), arXiv:1707.03451
  11. 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
  12. 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
  13. 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
  14. 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.
  15. 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
  16. 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
  17. 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.
  18. 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.
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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.
  25. M. P. Müller, J. Oppenheim, and O. C. O. Dahlsten, The black hole information problem beyond quantum theory, Journal of High Energy Physics 09, 116 (2012), arXiv:1206.5030
  26. J. Eisert, M. P. Müller, and C. Gogolin, Quantum measurement occurrence is undecidable, Phys. Rev. Lett. 108, 260501 (2012), arXiv:1111.3965
  27. 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
  28. 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
  29. 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
  30. C. Gogolin, M. P. Müller, and J. Eisert, Absence of thermalization in non-integrable systems, Phys. Rev. Lett. 106, 040401 (2011), arXiv:1009.2493
  31. Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011), arXiv:1004.1483
  32. 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
  33. M. Müller and D. Schleicher, How to add a noninteger number of terms: from axioms to new identities, American Mathematical Monthly 118(2), 136-152 (2011), arXiv:1001.4695
  34. N. Ay, M. Müller, and A. Szkola, Effective complexity of stationary process realizations, Entropy 13 (6), 1200-1211 (2011), arXiv:1001.2686
  35. 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
  36. 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
  37. M. Müller, Stationary algorithmic probability, Theoretical Computer Science 411, 113-130 (2010), arXiv:cs.IT/0608095
  38. M. Müller and D. Schleicher, Fractional sums and Euler-like identities, The Ramanujan Journal 21(2), 123-143 (2010), arXiv:math/0502109
  39. M. Müller, Convex trace functions on quantum channels and the additivity conjecture, Phys. Rev. A 79, 052332 (2009), arXiv:0809.4060
  40. 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
  41. M. Müller, Does probability become fuzzy in small regions of spacetime?, Phys. Lett. B 673, 166-167 (2009), arXiv:0712.4090
  42. M. Müller, On the quantum Kolmogorov complexity of classical strings, Int. J. Quant. Inf. 7 (4), 701-711 (2009), arXiv:0707.2924
  43. 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
  44. 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
  45. 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


Book chapters, comments, conference proceedings etc.

  1. 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.
  2. M. P. Müller, Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes), SciPost Phys. Lect. Notes 28 (2021), arXiv:2011.01286
  3. 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.
  4. 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
  5. 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
  6. 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
  7. M. P. Müller, A note on "Hamiltonian for the zeros of the Riemann zeta function", arXiv:1704.04705
  8. 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
  9. 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.
  10. 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
  11. 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.