Abstract
We show that a complex symmetric matrix of the form , where B is Hermitian positive semidefinite, has a nonnegative hafnian. Some positive scalar multiples of matrices A(Y, B) are encodable in a Gaussian boson sampler. Further, the hafnian of this matrix is non-decreasing in B in the sense that haf A(Y, L) ≥ haf A(Y, B) if
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Disclosure statement
No potential conflict of interest was reported by the author(s).