Research

The group works on the interface between quantum mechanics and other areas
of applied mathematics.

Our main emphasis lies on the application of rigorous mathematical methods to problems
in quantum information theory and many-body theory.

Conversely, we aim to use methods originating in quantum physics to classical problems,
e.g. in machine learning theory.

Featured Publications

data analysis using sparse and low-rank representations; compressed sensing.	Recovering low-rank matrices from few coefficients in any basis D. Gross IEEE Trans. on Information Theory 57, 1548 (2011) (arXiv) A partial derandomization of PhaseLift using spherical designs D. Gross, F. Krahmer, R. Kueng Journal of Fourier Analysis and Applications 21, 229 - 266 (arXiv)
mathematical physics	Index theory of one dimensional quantum walks and cellular automata D. Gross, V. Nesme, H. Vogts, R.F. Werner Commun. Math. Phys. 310, 419-454 (2012) (arXiv) Hudson's Theorem for finite-dimensional quantum systems D. Gross J. Math. Phys. 47, 122107 (2006) (arXiv)
quantum computation and quantum information	Measurement-based quantum computation beyond the one-way model D. Gross, J. Eisert, N. Schuch, and D. Perez-Garcia Phys. Rev. A 76, 052315 (2007) (arXiv) Entanglement Polytopes M. Walter, B. Doran, D. Gross, M. Christandl Science 340, 6137 (2013) (arXiv)
causal analysis	Inferring latent structures via information inequalities R. Chaves, L. Luft, T. O. Maciel, D. Gross, D. Janzing, B. Schölkopf Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI 2014), pp. 112 - 121, AUAI Press (arXiv) Information-Theoretic Implications of Quantum Causal Structures R. Chaves, C. Majenz, D. Gross Nature Communications 6, 5766 (arXiv)
foundations of quantum mechanics	Local orthogonality: a multipartite principle for correlations T. Fritz, B. Sainz, R. Augusiak, J. B. Brask, R. Chaves A. Leverrier, A, Acin Nat. Comm. 4, 3263 (2013) (arXiv) All reversible dynamics in maximally non-local theories are trivial D. Gross, M. Mueller, R. Colbeck, and O. Dahlsten Phys. Rev. Lett. 104, 080402 (2010) (arXiv)
foundations of  stat. mech.	Truly work-like work extraction via a single-shot analysis J. Aberg Nat. Comm. 4, 1925 (2013) (arXiv)
experimental collaborations	Probing the negative Wigner function of a pulsed single photon point by point K. Laiho, K. Cassemiro, D. Gross, C. Silberhorn Phys. Rev. Lett. 105, 253603 (2010) (arXiv) Permutationally invariant quantum tomography G. Toth, W. Wieczorek, D. Gross, R. Krischek, C. Schwemmer, H. Weinfurter Phys. Rev. Lett. 105, 250403 (2010) (arXiv)