Research

A main motivation for my research is to understand the role of information in physics. I work with the rigorous mathematical methods of quantum information theory and mathematical physics, in order to understand the principles of information processing and its implications for physics. Specifically, I am interested in

  • quantum statistical mechanics: measure concentration, thermalization,
  • non-local correlations and general probabilistic theories,
  • quantum and classical algorithmic complexity.

 

Selected publications

Ll. Masanes, M. P. Müller, "A derivation of quantum theory from physical requirements", New J. Phys. 13, 063001 (2011), http://arxiv.org/abs/1004.1483
(featured as "research highlight" in Nature Physics, Vol. 7, July 2011.)

C. Gogolin, M. P. Müller, J. Eisert, "Absence of thermalization in non-integrable systems", Phys. Rev. Lett. 106, 040401 (2011), http://arxiv.org/abs/1009.2493

M. P. Müller, D. Gross, J. Eisert, "Concentration of measure for quantum states with a fixed expectation value", Commun. Math. Phys., Vol. 303/3, 785-824 (2011), http://arxiv.org/abs/1003.4982

D. Gross, M. Müller, R. Colbeck, O. C. O. Dahlsten, "All reversible dynamics in maximally non-local theories are trivial", Phys. Rev. Lett. 104, 080402 (2010), http://arxiv.org/abs/0910.1840

M. Müller, "Strongly universal quantum Turing machines and invariance of Kolmogorov complexity
", IEEE Trans. Inf. Th., Vol. 54/2 pp. 763-780 (2008), http://www.arxiv.org/abs/quant-ph/0605030

F. Benatti, T. Krüger, M. Müller, Ra. Siegmund-Schultze, A. Szkola, "Entropy and quantum Kolmogorov complexity: a quantum Brudno's theorem", Commun. Math. Phys., Vol. 265/2 pp. 437-461 (2006), http://www.arxiv.org/abs/quant-ph/0506080

 

Further publications

Ll. Masanes, M. P. Müller, D. Perez-Garcia, R. Augusiak, "Entangling dynamics beyond quantum theory", http://arxiv.org/abs/1111.4060

J. Eisert, M. P. Müller, C. Gogolin, "Quantum measurement occurrence is undecidable", http://arxiv.org/abs/1111.3965

G. de la Torre, Ll. Masanes, A. J. Short, M. P. Müller, "Deriving quantum theory from its local structure and reversibility", http://arxiv.org/abs/1110.5482

M. P. Müller, C. Ududec, "The power of reversible computation determines the self-duality of quantum theory", http://arxiv.org/abs/1110.3516

M. P. Müller, O. C. O. Dahlsten, V. Vedral, "Unifying typical entanglement and coin tossing: on randomization in probabilistic theories", http://arxiv.org/abs/1107.6029

M. Müller, D. Schleicher, "How to add a non-integer number of terms: from axioms to new identities", American Mathematical Monthly Vol. 118, No. 2, pp. 136-152 (2011), http://arxiv.org/abs/1001.4695

M. Müller, "Stationary algorithmic probability", Theoretical Computer Science 411 pp. 113-130 (2010), doi:10.1016/j.tcs.2009.09.017, http://www.arxiv.org/abs/cs.IT/0608095

N. Ay, M. Müller, A. Szkola, "Effective complexity and its relation to logical depth", IEEE Trans. Inf. Th., Vol. 56/9 pp. 4593-4607 (2010), http://arxiv.org/abs/0810.5663

N. Ay, M. Müller, A. Szkola, "Effective Complexity of stationary process realizations", Entropy Vol. 13 No. 6, pp. 1200-1211 (2011), http://arxiv.org/abs/1001.2686

M. Müller, "Convex trace functions on quantum channels and the additivity conjecture", Phys. Rev. A 79, 052332 (2009), http://arxiv.org/abs/0809.4060

M. Müller, C. Rogers, R. Nagarajan, "Lossless quantum prefix compression for communication channels that are always open", Phys. Rev. A 79, 012302 (2009), http://arxiv.org/abs/0808.2003

M. Müller, D. Schleicher, "Fractional sums and Euler-like identities", The Ramanujan Journal, Vol. 21, Issue 2, pp. 123-143 (2010), http://www.arxiv.org/abs/math/0502109

M. Müller, C. Rogers, "Quantum bit strings and prefix-free Hilbert spaces",
ITSL '08 (Information Theory and Statistical Learning) conference proceedings, http://arxiv.org/abs/0804.0022

M. Müller, "Does probability become fuzzy in small regions of spacetime?", Phys. Lett. B 673, 166-167(2009), http://arxiv.org/abs/0712.4090

M. Müller, "On the quantum Kolmogorov complexity of classical strings", Int. J. Quant. Inf., Vol. 7/4 pp. 701-711 (2009), http://www.arxiv.org/abs/0707.2924

M. Müller, D. Schleicher, "How to add a non-integer number of terms, and how to produce unusual infinite summations", Journal of Computational and Applied Mathematics, Vol. 178/1-2 pp 347-360 (2005), HowToAdd.pdf

As a highschool student and undergraduate, I was working on sums with a non-integer number of addends (yielding unusual identities) and some different topics that are described here.

Theses

doctoral thesis (2007): "Quantum Kolmogorov complexity and the quantum Turing machine", http://arxiv.org/abs/0712.4377
http://opus.kobv.de/tuberlin/volltexte/2007/1655/

diploma thesis (2004): "Das Quanten-Shannon-McMillan-Breiman-Theorem am Beispiel der Heisenbergschen Spinkette" (only in German), diplomarbeit.pdf




Popular scientific


Gebändigter Zufall
Verbundjournal, Juni 2006, S. 14 f., verbund66.pdf
(p. 14/15, German)

Geschärfter Blick ins Gehirn
Verbundjournal, September 2005, S. 10 f., verbund63.pdf
(p. 10/11, German)