Analytic Gaussian formulas for the symmetric quantum Barankin bound

Establish analytic formulas for the matrix elements of the symmetric quantum Barankin bound for Gaussian states in terms of their mean vectors and covariance matrices.

Background

The paper develops analytic mean-vector and covariance-matrix formulas for the right-division quantum Barankin bound of Gaussian states. The authors contrast this achievement with the symmetric-division quantum Barankin bound, whose evaluation generally relies on more difficult operator-level calculations and for which corresponding Gaussian formulas are not available in the paper.

The unresolved problem is to obtain an analogous closed-form representation for the symmetric quantum Barankin matrix, thereby enabling efficient evaluation and comparison of the symmetric bound for Gaussian states.