TY  - JOUR
A1  - Ohliger, Matthias
A1  - Nesme, V.
A1  - Eisert, J.
T1  - Efficient and feasible state tomography of quantum many-body systems
JF  - New journal of physics : the open-access journal for physics
N2  - We present a novel method for performing quantum state tomography for many-particle systems, which are particularly suitable for estimating the states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need to measure a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary two-designs, i.e. certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established experimental techniques such as optical super-lattices, laser speckles and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. This is possible without the need to address single sites in any step of the procedure. Combining our approach with tensor network methods-in particular, the theory of matrix product states-we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing, in principle, to perform tomography on large-scale systems readily available in present experiments.
Y1  - 2013
U6  - https://doi.org/10.1088/1367-2630/15/1/015024
SN  - 1367-2630
VL  - 15
IS  - 5
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -