Adaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomography
含噪量子零差层析中 Wigner 函数的自适应上确界范数估计
In quantum optics, the quantum state of a light beam is represented through the Wigner function, a density on $\mathbb{R}^{2}$, which may take negative values but must respect intrinsic positivity constraints imposed by quantum physics. In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2<\eta\leq1$, we study the theoretical performance of a kernel estimator of the Wigner function. We prove that it is minimax efficient, up to a logarithmic…