Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements

Finding the optimal attainable precisions in quantum multiparameter metrology is a non-trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramér–Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work, we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on a finite number of copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite programme. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.

Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate. In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.

Stochastic Restricted Liu Type estimator for SUR model

In this paper, we introduce new Stochastic Restricted Estimator for SUR model, defined by Stochastic Restricted Liu Type SUR estimator (SRLTSE) . The propose estimator has deal with multicollinearity in SUR model if there is a degree of uncertainty in the parameters restriction. Moreover, the superiority of (SRLTSE) estimator was derived with respect to mean squared error matrix (MSEM) criteria. Finally, a simulation study was conducted. This simulation used standard mean squares error (MSE) criterion to illustrate the advantage between Stochastic Restricted SUR estimator (SRSE), Stochastic Restricted Ridge SUR estimator (SRRSE), and Stochastic Restricted Liu Type SUR estimator (SRLTSE) at several factors.Â