Quantum state tomography via compressed sensing

  • 18 September 2009
Abstract
We establish novel methods for quantum state and process tomography based on compressed sensing. Our protocols require only simple Pauli measurements, and use fast classical post-processing based on convex optimization. Using these techniques, it is possible to reconstruct an unknown density matrix of rank r using O(rd log^2 d) measurement settings, a significant improvement over standard methods that require d^2 settings. The protocols are stable against noise, and extend to states which are approximately low-rank. The acquired data can be used to certify that the state is indeed close to a low-rank one, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations.

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