Quantum state tomography via compressed sensing

Details Quantum state tomography via compressed sensing Quantum state tomography via compressed sensing

2009-09-18

arxiv.org/abs/0909.3304v4

Phys. Rev. Lett. 105, 150401 (2010)

Physics

Quantum Physics

4 pages, 1 figure; v3, v4: presentation improved

Scientific paper

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.

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