title: Quantum state tomography via compressed sensing.
abstract: 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(rdlog²d) measurement settings, compared to standard methods that require d² 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.
authors.affiliation: Institute for Theoretical Physics, Leibniz University Hannover, 30167 Hannover, Germany.
authors.forename: David
authors.initials: D
authors.lastname: Gross
authors.forename: Yi-Kai
authors.initials: YK
authors.lastname: Liu
authors.forename: Steven T
authors.initials: ST
authors.lastname: Flammia
authors.forename: Stephen
authors.initials: S
authors.lastname: Becker
authors.forename: Jens
authors.initials: J
authors.lastname: Eisert