English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We estimate the quantum state of a light beam from results of quantumhomodyne measurements performed on identically prepared quantum systems. Thestate is represented through the Wigner function, a generalized probabilitydensity on $\mathbb{R}^2$ which may take negative values and must respectintrinsic positivity constraints imposed by quantum physics. The effect of thelosses due to detection inefficiencies, which are always present in a realexperiment, is the addition to the tomographic data of independent Gaussiannoise. We construct a kernel estimator for the Wigner function, prove that itis minimax efficient for the pointwise risk over a class of infinitelydifferentiable functions, and implement it for numerical results. We constructadaptive estimators, that is, which do not depend on the smoothness parameters,and prove that in some setups they attain the minimax rates for thecorresponding smoothness class.

Minimax and adaptive estimation of the Wigner function in quantum homodyne tomography with noisy data