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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We estimate the quantum state of a light beam from results of quantumhomodyne measurements performed on identically prepared pulses. The state isrepresented through the Wigner function, a ``quasi-probability density'' on$\mathbb{R}^{2}$ which may take negative values and must respect intrinsicpositivity constraints imposed by quantum physics. The data consists of $n$i.i.d. observations from a probability density equal to the Radon transform ofthe Wigner function. We construct an estimator for the Wigner function, andprove that it is minimax efficient for the pointwise risk over a class ofinfinitely differentiable functions. A similar result was previously derived byCavalier in the context of positron emission tomography. Our work extends thisresult to the space of smooth Wigner functions, which is the relevant parameterspace for quantum homodyne tomography.Comment: 15 page

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors