Correction to: Scientific Reports https://doi.org/10.1038/s41598-023-43811-6, published online 03 October 2023

The original version of this Article contained errors.

Equation 12 was incorrectly given as:

$$\begin{array}{c}\eta (t)=\frac{1}{g}[g\tau -1+{\text{exp}}\,[-g\tau ]]\end{array}$$

The correct Equation 12 appears below.

$$\eta (t)=\frac{1}{g}[gt-1+{\text{exp}}\,[-gt]]$$

In addition, in the Physical model section, under the subheading ‘Classical noisy procedure’.

“Note that \(\hat{{\rho }_{32}^{*}}=\hat{{\rho }_{23}}={\rho }_{23}{\text{exp}}\,[-\frac{4(\gamma t+{e}^{\gamma (-t)}-1)}{\gamma }]\).”

now reads:

“Note that \(\hat{{\rho }_{32}^{*}}=\hat{{\rho }_{23}}={\rho }_{23}{\text{exp}}\,[-\frac{4(gt+{e}^{g(-t)}-1)}{g}]\).”

The original Article has been corrected.