Further simplification of Gaussian right-division Barankin formulas

Derive further simplifications of the analytic Gaussian-state formulas for the right-division quantum Barankin matrix and its recovery of the right logarithmic derivative quantum Cramér–Rao bound.

Background

The paper derives explicit expressions for the right-division quantum Barankin matrix of Gaussian states using mean vectors, covariance matrices, and products of Gaussian operators. It also discusses the limiting recovery of the right logarithmic derivative quantum Cramér–Rao bound.

Although the authors numerically verify this recovery, they report that the resulting expressions are cumbersome and that they could not simplify them further. This leaves open the problem of finding more tractable analytic forms.