This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown scalar coefficient (denoted by $\beta$), and the error is a random operator. In the course of this study, we propose a quantum version of a class of estimators (denoted by $M$ estimator) of $\beta$, and the large sample behaviour of those quantum version of the estimators are derived, given the fact that the true model is also linear and the samples are observed eigenvalue pairs of the operator valued observables.

翻译：本文介绍了量子概率中的算子对算子回归模型。在该回归模型中，响应变量与自变量均为特定的算子值可观测量，它们通过未知标量系数（记为 $\beta$）线性关联，且误差项为一随机算子。在此研究过程中，我们提出了一类估计量（记为 $M$ 估计量）的量子版本用于估计 $\beta$，并在真实模型同样为线性且观测样本为算子值可观测量的特征值对的条件下，推导了这些量子版本估计量的大样本性质。