Tuesday, 01 February, 2011
Group Seminar MPQ: Learning a lot from a little: Measuring entanglement in and efficient quantum state tomography of many-body systems
Tuesday, 01.02.2011 10 a.m. (s.t.) in Herbert-Walther-lecture room, MPQ Garching
Dr. Marcus Cramer, Plenio's Group, Institute of Theoretical Physics, Uni-Ulm
In this talk I will report on some recent results concerning (i) ways to quantify entanglement in many-body systems using simple measurements and (ii) efficient reconstruction of quantum states from local measurements.
(i): I will present a scheme that requires no assumptions on the state in the laboratory and show how a lower bound to the entanglement can, in the case of spin systems, be read off directly from the scattering cross section of Neutrons deflected from solid state samples and the time-of-flight distribution in the case of bosons in optical lattices.
(ii): I will show how one can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. Our scheme requires only a linear number of local measurements and classical postprocessing that is polynomial in the system size. A further strength of the method is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.