For an overview, please see the pages of my research
group at IQOQI Vienna.
- 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
Alert, two blog posts in English language (#1 and
There is also an excellent description of our work in
German by Martin Bäker on his blog "Hier
- Faster than allowed by quantum computing?
(Answer: no!) Marius' and my publication 49 below has
received some media attention, including the Austrian
Standard (see also here
Medicine Network (yes, that's somewhat
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).
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
- Our results on the Berry-Keating conjecture
(paper 43) have been greatly exaggerated by some media
Wire), which in turn has led to criticism (e.g.
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
Reference Frame, phys.org,
- 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.
Scientist, September 25, 2013. Discusses some
approaches towards this question, including our
publication 32 below.
- Quantum causality: information insights.
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
- 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
- More discussions online: Jess
Riedel's blog, Physics
blog, Stack Exchange (here
Preprints on arXiv
- C. L. Jones, S. L. Ludescher, A. Aloy, and M. P.
Müller, Theory-independent randomness generation
with spacetime symmetries, arXiv:2210.14811
- M. P. Müller and A. J. P. Garner, Testing
quantum theory with generalized noncontextuality,
- A. de la Hamette, S. L. Ludescher, and M. P. Müller,
Entanglement/Asymmetry correspondence for internal
quantum reference frames, arXiv:2112.00046
- 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
- M. Krumm and M. P. Müller, Computational
irreducibility and compatibilism: towards a
- P. A. Höhn, M. P. Müller, C. Pfeifer, and D. Rätzel,
A local quantum Mach principle and the metricity of
- 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
- 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
- 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
- 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
- M. P. Müller, Law without law: from observer
states to physics via algorithmic information theory,
Quantum 4, 301 (2020), arXiv:1712.01826
- 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
- M. Lostaglio and M. P. Müller, Coherence and
asymmetry cannot be broadcast, Phys. Rev. Lett.
123, 020403 (2019), arXiv:1812.08214
- 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
- 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
- M. Krumm and M. P. Müller, Quantum computation
is the unique reversible circuit model for which
bits are balls, npj Quantum Inf. 5, 7
- J. Riddell and M. P. Müller, Generalized
eigenstate typicality in translation-invariant
quasifree fermionic models, Phys. Rev. B 97,
035129 (2018), arXiv:1709.05569
- M. P. Müller, Correlating thermal machines and
the second law at the nanoscale, Phys. Rev. X 8,
041051 (2018), arXiv:1707.03451
- 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
- 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),
- M. Krumm, H. Barnum, J. Barrett, and M. P. Müller, Thermodynamics and the
structure of quantum theory, New J. Phys. 19, 043025 (2017),
- 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.
- 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
- M. P. Müller and M. Pastena, A generalization
of majorization that characterizes Shannon entropy,
IEEE Trans. Inf. Th. 62(4),
- 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
- M. Lostaglio, M. P. Müller, and M. Pastena, Stochastic
as a resource in small-scale thermodynamics,
Phys. Rev. Lett. 115, 150402 (2015),
arXiv:1409.3258. PRL: Editor's Suggestion.
- M. P. Müller, E. Adlam, Ll. Masanes, and N. Wiebe, Thermalization
canonical typicality in translation-invariant
quantum lattice systems, Commun. Math. Phys. 340(2),
499-561 (2015), arXiv:1312.7420
- 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
- H. Barnum, J. Barrett, M. Krumm, and M. P. Müller, Entropy,
and thermodynamics in general probabilistic theories,
Electronic Proceedings in Theoretical Computer Science
195, 43-58 (2015), arXiv:1508.03107
- H. Barnum, M. P. Müller, and C. Ududec, Higher-order
and single-system postulates characterizing quantum
theory, New J. Phys. 16,
123029 (2014), arXiv:1403.4147
- 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
- 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
- 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
- M. P. Müller, J. Oppenheim, and O. C. O. Dahlsten, The
hole information problem beyond quantum theory,
J. High Energy Phys. 09, 116 (2012),
- J. Eisert, M. P. Müller, and C. Gogolin,
Quantum measurement occurrence is undecidable,
Phys. Rev. Lett. 108, 260501 (2012),
- 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
- 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
- M. P. Müller, O. C. O. Dahlsten, and V. Vedral, Unifying
entanglement and coin tossing: on randomization in
probabilistic theories, Commun. Math. Phys. 316(2),
- C. Gogolin, M. P. Müller, and J. Eisert, Absence
of thermalization in non-integrable systems,
Phys. Rev. Lett. 106, 040401 (2011),
- Ll. Masanes and M. P. Müller, A derivation of
quantum theory from physical requirements, New
J. Phys. 13, 063001 (2011), arXiv:1004.1483
- M. P. Müller, D. Gross, and J. Eisert, Concentration
measure for quantum states with a fixed expectation
value, Commun. Math. Phys. 303(3),
785-824 (2011), arXiv:1003.4982
- 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
- N. Ay, M. Müller, and A. Szkola, Effective
complexity of stationary process realizations,
Entropy 13 (6), 1200-1211 (2011), arXiv:1001.2686
- 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
- N. Ay, M. Müller, and A. Szkola, Effective
complexity and its relation to logical depth,
IEEE Trans. Inf. Th. 56(9), 4593-4607
- M. Müller, Stationary algorithmic probability,
Theor. Comput. Sci. 411, 113-130
- M. Müller and D. Schleicher, Fractional sums
and Euler-like identities, Ramanujan J.
21(2), 123-143 (2010), arXiv:math/0502109
- M. Müller, Convex trace functions on quantum
channels and the additivity conjecture, Phys.
Rev. A 79, 052332 (2009), arXiv:0809.4060
- 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
- M. Müller, Does probability become fuzzy in
small regions of spacetime?, Phys. Lett. B 673,
166-167 (2009), arXiv:0712.4090
- M. Müller, On the quantum Kolmogorov complexity
of classical strings, Int. J. Quant. Inf. 7
(4), 701-711 (2009), arXiv:0707.2924
- M. Müller, Strongly universal quantum Turing
machines and invariance of Kolmogorov complexity,
IEEE Trans. Inf. Th. 54(2), 763--780
- 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),
- 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
- 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.
- M. P. Müller, Probabilistic Theories and
Reconstructions of Quantum Theory (Les Houches 2019
lecture notes), SciPost Phys. Lect. Notes 28
- 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.
- 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
- 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
- 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
- M. P. Müller, A
note on "Hamiltonian for the zeros of the Riemann
zeta function", arXiv:1704.04705
- M. P. Müller, J. Oppenheim, and O. C. O. Dahlsten, Hiding
in theories beyond quantum mechanics, and its
application to the black hole information problem,
Horizons of Quantum Physics Conference Proceedings, Foundations
Physics, Springer, 2014.
- M. P. Müller and Ll. Masanes, Information-theoretic
for quantum theory, in "Quantum Theory:
Informational Foundations and Foils", G. Chiribella
and R. W. Spekkens (editors), Springer, 2016, arXiv:1203.4516
- 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
Beispiel der Heisenbergschen Spinkette (2004).
Grade: very good.
Science writing by myself (about work by
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
- 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.