Research interests

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

Media coverage

• The Born rule has been derived from simple physical principles. Quanta magazine, February 2019. Discusses publication 51 below (with Lluís Masanes and Thomas Galley), and related work by Adán Cabello. See also the article on Science Alert, two blog posts in English language (#1 and #2), and piqd.de. There is also an excellent description of our work in German by Martin Bäker on his blog "Hier wohnen Drachen".
  
  
• Faster than allowed by quantum computing? (Answer: no!) Marius' and my publication 49 below has received some media attention, including the Austrian newspaper Der Standard (see also here and here), APA, Tiroler Tageszeitung, BrightSurf.com, R&D Magazine, Health Medicine Network (yes, that's somewhat surprising...), phys.org, Space Daily, innovations-report, newswise, EurekAlert! and others. Note that our work builds very strongly on earlier work, ideas, and insights by Lluís Masanes, Gonzalo de la Torre, and Tony Short (see in particular publication 29 below).
  

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  Thermal machines and second law in the quantum realm. News item by the IQOQI Vienna on my PRX publication 47 below. Best Paper Award 2019 by the Austrian Academy of Sciences. The illustration is by the Viennese artist Christian Murzek. Builds on earlier work with Matteo Lostaglio and my student Michele Pastena, see articles 39 and 41. See also the follow-up work on the catalytic entropy conjecture with Paul Boes, Jens Eisert, Rodrigo Gallego, and Henrik Wilming (paper 50), featured in this press release.
  

• This ‘zero-worlds’ theory might just be crazy enough to be true. Interview with "Essentia Foundation", July 2021, on my approach summarized in paper 54 below. See also the New Scientist title story of November 2017, and New Scientist, January 2020 on "reality". There is also a Less Wrong blog post and this FQXi article from January 2019, and an article in the Israeli newspaper Haaretz. For a first introduction to this approach, feel free to have a look at this seminar talk on YouTube. Further posts include one by Ian Durham (FQXi) and a mention on a blog on Learning Machines.
  

• 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, phys.org, 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).

• Classical problem becomes undecidable in a quantum setting. Phys.org, July 2012. Popular-scientific description of publication 30 below. See also this FQXi article (Searching for the Impossible) from January 2015, and see the related independent and more extensive works by Toby Cubitt, David Pérez-García and Michael Wolf, including this amazing result.
  
  
• And thus the quantum. Nature Physics 7, 519 (2011) research highlights. This features our publication 25, where we show that the Hilbert space formalism of quantum theory can be reconstructed from five simple physical/information-theoretic postulates.
  
  
• More discussions online: Jess Riedel's blog, Physics arXiv blog, John Baez' blog, Howard Barnum's blog, Stack Exchange (here and here), forum.intelligence.org, Компьютерное Обозрение.
  

Preprints on arXiv

65. C. L. Jones, S. L. Ludescher, A. Aloy, and M. P. Müller, Theory-independent randomness generation with spacetime symmetries, arXiv:2210.14811
    
66. M. P. Müller and A. J. P. Garner, Testing quantum theory with generalized noncontextuality, arXiv:2112.09719
    
67. 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
    
68. P. A. Höhn, M. P. Müller, C. Pfeifer, and D. Rätzel, A local quantum Mach principle and the metricity of spacetime, arXiv:1811.02555
    

Peer-reviewed publications

61. 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
62. 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
63. 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
64. 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
65. 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
66. 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
67. M. P. Müller, Law without law: from observer states to physics via algorithmic information theory, Quantum 4, 301 (2020), arXiv:1712.01826
68. 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
69. M. Lostaglio and M. P. Müller, Coherence and asymmetry cannot be broadcast, Phys. Rev. Lett. 123, 020403 (2019), arXiv:1812.08214
70. 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
71. 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
72. 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
73. J. Riddell and M. P. Müller, Generalized eigenstate typicality in translation-invariant quasifree fermionic models, Phys. Rev. B 97, 035129 (2018), arXiv:1709.05569
74. M. P. Müller, Correlating thermal machines and the second law at the nanoscale, Phys. Rev. X 8, 041051 (2018), arXiv:1707.03451
75. 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
76. 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
    
77. 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
78. 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.
79. 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
    
80. 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
81. 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.
82. 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.
83. 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
84. 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
85. 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
86. 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
87. 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
88. 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
89. 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.
90. 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
    
91. J. Eisert, M. P. Müller, and C. Gogolin, Quantum measurement occurrence is undecidable, Phys. Rev. Lett. 108, 260501 (2012), arXiv:1111.3965
92. 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
93. 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
94. 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
95. C. Gogolin, M. P. Müller, and J. Eisert, Absence of thermalization in non-integrable systems, Phys. Rev. Lett. 106, 040401 (2011), arXiv:1009.2493
96. Ll. Masanes and M. P. Müller, A derivation of quantum theory from physical requirements, New J. Phys. 13, 063001 (2011), arXiv:1004.1483
    
97. 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
98. 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
99. N. Ay, M. Müller, and A. Szkola, Effective complexity of stationary process realizations, Entropy 13 (6), 1200-1211 (2011), arXiv:1001.2686
100. 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
101. 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
102. M. Müller, Stationary algorithmic probability, Theor. Comput. Sci. 411, 113-130 (2010), arXiv:cs.IT/0608095
103. M. Müller and D. Schleicher, Fractional sums and Euler-like identities, Ramanujan J. 21(2), 123-143 (2010), arXiv:math/0502109
104. M. Müller, Convex trace functions on quantum channels and the additivity conjecture, Phys. Rev. A 79, 052332 (2009), arXiv:0809.4060
105. 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
106. M. Müller, Does probability become fuzzy in small regions of spacetime?, Phys. Lett. B 673, 166-167 (2009), arXiv:0712.4090
107. M. Müller, On the quantum Kolmogorov complexity of classical strings, Int. J. Quant. Inf. 7 (4), 701-711 (2009), arXiv:0707.2924
108. 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
109. 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
110. 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

11. T. D. Galley, Ll. Masanes, and M. P. Müller, Reply to "Masanes-Galley-Müller and the State-Update Postulate", arXiv:2212.03629
    
12. 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.
13. M. P. Müller, Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes), SciPost Phys. Lect. Notes 28 (2021), arXiv:2011.01286
14. 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.
    
15. 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
16. 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
17. 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
18. M. P. Müller, A note on "Hamiltonian for the zeros of the Riemann zeta function", arXiv:1704.04705
19. 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.
20. 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
21. M. Müller and C. Rogers, Quantum bit strings and prefix-free Hilbert spaces, ITSL '08 conference proceedings, arXiv:0804.0022

Theses

• 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)

• Gebändigter Zufall ("Subdued randomness"), Verbundjournal 06/2006, p. 14 f.
• Geschärfter Blick ins Gehirn ("Sharp view on the brain"), Verbundjournal 09/2005, p. 10 f.

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.