%0 Journal Article
%J Physical Review Letters
%D 2010
%T Quantum state tomography via compressed sensing
%A David Gross
%A Yi-Kai Liu
%A Steven T. Flammia
%A Stephen Becker
%A Jens Eisert
%X We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rd log^2 d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low-rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations.
%B Physical Review Letters
%V 105
%8 2010/10/4
%G eng
%U http://arxiv.org/abs/0909.3304v4
%N 15
%! Phys. Rev. Lett.
%R 10.1103/PhysRevLett.105.150401