@article{OhligerNesmeEisert2013,
  author    = {Ohliger, Matthias and Nesme, V. and Eisert, J.},
  title     = {Efficient and feasible state tomography of quantum many-body systems},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {15},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {5},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/15/1/015024},
  pages     = {19},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@article{deBeaudrapOhligerOsborneetal.2010,
  author    = {de Beaudrap, Niel and Ohliger, Matthias and Osborne, Tobias J. and Eisert, Jens},
  title     = {Solving frustration-free spin systems},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.105.060504},
  year      = {2010},
  abstract  = {We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean- field theory.},
  language  = {en}
}
@phdthesis{Ohliger2012,
  author    = {Ohliger, Matthias},
  title     = {Characterizing and measuring properties of continuous-variable quantum states},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-62924},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis.},
  language  = {en}
}