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 -