Continuous-variable quantum compressed sensing

Details Continuous-variable quantum compressed sensing Continuous-variable quantum compressed sensing

2011-11-03

arxiv.org/abs/1111.0853v2

Physics

Quantum Physics

30 pages, 3 figures; Section 5 with new results added; author added; minor changes in presentation

Scientific paper

We introduce a novel method to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. The method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise.

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