- Working Paper
We introduce a novel method to faithfully reconstruct unknown quantum states that are close to low-rank states by few measurement settings only. 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 not necessarily pairwise orthogonal, but can be taken from a so-called tight frame - covering hence most meaningful measuring scenarios. As continuous-variable states and measurements are most ubiquitous in the optical setting, we discuss the reconstruction of states of multi-mode light in great detail and show the advantage of the proposed technique over present methods for quantum-optical state reconstruction, as well as its robustness under noise. We finally introduce a method to construct a certificate which guarantees the success of the reconstruction with an efficient algorithm with no assumption on the state Show more
Organisational unit03879 - Christandl, Matthias (SNF-Professur)
NotesSubmitted 3 November 2011.
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