Quantum Information and Entanglement Theory

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?

  • 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?

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?

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.

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.