@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}
}