Controlled quantum dynamics is concerned with the preparation, control, read-out, and verification of composite quantum systems. This raises considerable experimental challenges but also leads us, quite naturally, to questions concerning the mathematical structure of states, dynamics and correlations in composite quantum systems.
What are for example the most suitable mathematical structures for the description of the states and evolution of composite quantum systems or quantum many-body systems? Can we make use of this knowledge to efficiently learn the state of a many-body system?

• Scalable reconstruction of density matrices, T. Baumgratz, D. Gross, M. Cramer, and M.B. Plenio, Physical Review Letters 111, 020401 (2013) and arXiv:1207.0358,

• Efficient quantum state tomography, M. Cramer, M.B. Plenio, S.T. Flammia, R. Somma, D. Gross, S.D. Bartlett, O. Landon-Cardinal, D. Poulin, and Y.-K. Liu, Nat. Commun. 1, 149 (2010).

How efficiently can we manipulate quantum states under constrained sets of operations? Is there a quantitative theory of quantum correlations a.k.a. entanglement and how is it related for example to thermodynamics and statistical mechanics?

• An introduction to entanglement measures, M. B. Plenio and S. Virmani, Quantum Information and Computation 7, 1 (2007),

• Area laws for the entanglement entropy – A review, J. Eisert, M. Cramer and M. B. Plenio, Reviews of Modern Physics 82, 277 (2010),

• A Generalization of Quantum Stein’s Lemma, F.G.S.L. Brandao and M. B. Plenio, Communications in Mathematical Physics 295, 791 (2010),

• Entanglement Theory and the Second Law, F.G.S.L. Brandao and M. B. Plenio, Nature Physics 4, 873 (2008).

Can we infer properties of many-body quantum states (such as entanglement) without making unproven assumptions and taking into account that experimentally available measurements are often quite constrained by experimental requirements?

• Measuring entanglement in condensed matter systems, M. Cramer, M.B. Plenio, and H. Wunderlich, Phys. Rev. Lett. 106, 020401 (2011),

• Optimal verification of entanglement in a photonic cluster state experiment, H. Wunderlich, G. Vallone, P. Mataloni, M. B. Plenio, New J. Phys. 13, 033033 (2011).

If we wish to determine the properties of quantum states then we need to use detectors and other quantum devices. In the quantum domain these devices are complex themselves and we need to find efficient methods to characterize them. And this task, quantum detector tomography, needs to be achieved with the least experimental effort.

• Tomography of quantum detectors, J.S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K.L. Pregnell, C. Silberhorn, T.C. Ralph, J. Eisert, M.B. Plenio, and I.A. Walmsley, Nat. Phys. 5, 27 (2009).
• Mapping coherence in measurement: Full quantum tomography of a hybrid optical detector. L. Zhang, H.B. Coldenstrodt-Ronge, A. Datta, G. Puentes, J.S. Lundeen, X.M. Jin, B.J. Smith, M.B. Plenio and I.A. Walmsley. Nature Photonics 6, 364 – 368 (2012)

Our group explores all of the above questions, and some more, within the framework of entanglement theory. This work provides the technical and conceptual underpinning for many research problems that we are pursuing in this group.