TY - JOUR T1 - Quantum state tomography via compressed sensing JF - Physical Review Letters Y1 - 2010 A1 - David Gross A1 - Yi-Kai Liu A1 - Steven T. Flammia A1 - Stephen Becker A1 - Jens Eisert AB - 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. VL - 105 UR - http://arxiv.org/abs/0909.3304v4 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.105.150401 ER -