



01338nas a2200169   4500008004100000245005200041210005200093260001400145490000800159520087000167100001701037700001601054700002401070700002001094700001701114856003701131       2010                        eng d00aQuantum state tomography via compressed sensing0 aQuantum state tomography via compressed sensing  c2010/10/40 v1053 a  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.
1 aGross, David1 aLiu, Yi-Kai1 aFlammia, Steven, T.1 aBecker, Stephen1 aEisert, Jens  uhttp://arxiv.org/abs/0909.3304v4