@article{MuellerGrossEisert2011,
  author    = {M{\"u}ller, Markus P. and Gross, David and Eisert, Jens},
  title     = {Concentration of Measure for Quantum States with a Fixed Expectation Value},
  series = {Communications in mathematical physics},
  volume    = {303},
  journal   = {Communications in mathematical physics},
  number    = {3},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-011-1205-1},
  pages     = {785 -- 824},
  year      = {2011},
  abstract  = {Given some observable H on a finite-dimensional quantum system, we investigate the typical properties of random state vectors vertical bar psi >> that have a fixed expectation value < psi vertical bar H vertical bar psi > = E with respect to H. Under some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.},
  language  = {en}
}
@article{MasanesMueller2011,
  author    = {Masanes, Lluis and M{\"u}ller, Markus P.},
  title     = {A derivation of quantum theory from physical requirements},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {13},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {1},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/13/6/063001},
  pages     = {29},
  year      = {2011},
  abstract  = {Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements-the principles of relativity and light speed invariance-are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.},
  language  = {en}
}
@article{GogolinMuellerEisert2011,
  author    = {Gogolin, Christian and M{\"u}ller, Markus P. and Eisert, Jens},
  title     = {Absence of thermalization in nonintegrable systems},
  series = {Physical review letters},
  volume    = {106},
  journal   = {Physical review letters},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.106.040401},
  pages     = {4},
  year      = {2011},
  abstract  = {We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.},
  language  = {en}
}