Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $\mathrm{haf}A(Y,L) \ge \mathrm{haf}A(Y,B)$ if $L \succeq B$.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ