Nonnegativity for hafnians of certain matrices

We show that a complex symmetric matrix of the form $A(Y,B) = \begin{bmatrix}Y & B\ B^\top & \overline{Y} \end{bmatrix},$where$B$ is Hermitian positive semidefinite, has a nonnegative hafnian. These are positive scalar multiples of matrices $A(Y,B)$ that are encodable in a Gaussian boson sampler. Further, the hafnian of this matrix is non-decreasing in $B$ in the sense that $\mathrm{h}\mathrm{a}\mathrm{f}A(Y,L)\ge \mathrm{h}\mathrm{a}\mathrm{f}A(Y,B)$ if $L⪰B$.