Quantum state tomography via compressed sensing

TitleQuantum state tomography via compressed sensing
Publication TypeJournal Article
Year of Publication2010
AuthorsGross, D, Liu, Y-K, Flammia, ST, Becker, S, Eisert, J
JournalPhysical Review Letters
Date Published2010/10/4

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.

Short TitlePhys. Rev. Lett.