We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of teleportation when one of the observers undergoes non-uniform motion for a finite time. The upper bound to the optimal fidelity is degraded due to the observer's motion however, we discuss how this degradation can be corrected. These effects are observable for experimental parameters that are within reach of cutting-edge superconducting technology. Our setup will further provide guidance for future space-based experiments.Comment: 5 pages, 4 figures, minor deviations from published version. I.F. previously published as Ivette Fuentes-Guridi and Ivette Fuentes-Schulle

PACS 72.15.Rn -Localization effects (Anderson or weak localization) PACS 05.45.Mt -Quantum chaos; semiclassical methods PACS 71.30.+h -Metal-insulator transitions and other electronic transitions PACS 05.30.-d -Quantum statistical mechanicsAbstract -We consider eigenvectors of the Hamiltonian H0 perturbed by a generic perturbation V modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in V and valid for an arbitrary deterministic H0. Further we generalise them to the case of a random H0, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations.

We study the eigenvalues and the eigenvectors of N ×N structured random matrices of the form H = WHW +D with diagonal matrices D and W andH from the Gaussian Unitary Ensemble. Using the supersymmetry technique we derive general asymptotic expressions for the density of states and the moments of the eigenvectors. We find that the eigenvectors remain ergodic under very general assumptions, but a degree of their ergodicity depends strongly on a particular choice of W and D. For a special case of D = 0 and random W , we show that the eigenvectors can become critical and are characterized by non-trivial fractal dimensions.

We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices H = WHW , whereH is a random matrix from Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the moments and the distribution function of the eigenvectors components for a generic matrix W . We show that specific choices of W can modify significantly the nature of the eigenvectors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations.