State estimation in quantum homodyne tomography with noisy data

Abstract

In the framework of noisy quantum homodyne tomography with efficiency parameter $0<\eta \le 1$, we propose two estimators of a quantum state whose density matrix elements ${\rho }_{m,n}$ decrease like $e^{-B(m+n{)}^{r/2}}$, for fixed known $B>0$ and $0<r\le 2$. The first procedure estimates the matrix coefficients by a projection method on the pattern functions (that we introduce here for $0<\eta \le 1/2$), the second procedure is a kernel estimator of the associated Wigner function. We compute the convergence rates of these estimators, in ${\mathbb{L}}_2$ risk.

Cited by in corpus (1)

• Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data