2009/09/30 by David Gross, Yi-Kai Liu, Steven T. Flammia +2 · 4 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.105.150401
published as Phys. Rev. Lett. 105, 150401 (2010) · 4 pages, 1 figure; v3, v4: presentation improved
arxiv created 2010/08/16 · arxiv updated 2015/05/14
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 log2 d) 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. We present both theoretical bounds and numerical simulations.