We show that, for a class of planar determinantal point processes (DPP)\documentclass[12pt]{minimal}
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				\begin{document}$$ {\mathcal {X}}$$\end{document}X, the growth of the entanglement entropy\documentclass[12pt]{minimal}
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				\begin{document}$$S({\mathcal {X}}(\Omega )) $$\end{document}S(X(Ω))of\documentclass[12pt]{minimal}
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				\begin{document}$${\mathcal {X}}\ $$\end{document}Xon a compact region\documentclass[12pt]{minimal}
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				\begin{document}$$\Omega \subset {\mathbb {R}}^{2d}$$\end{document}Ω⊂R2d, is related to the variance\documentclass[12pt]{minimal}
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				\begin{document}$${\mathbb {V}}\left( {\mathcal {X}}(\Omega )\right) $$\end{document}VX(Ω)as follows:\documentclass[12pt]{minimal}
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				\begin{document}$$\begin{aligned} {\mathbb {V}}\left( {\mathcal {X}}(\Omega )\right) \lesssim S\left( \mathcal {X(} \Omega \mathcal {)}\right) \lesssim {\mathbb {V}}\left( {\mathcal {X}}(\Omega )\right) . \end{aligned}$$\end{document}VX(Ω)≲SX(Ω)≲VX(Ω).Therefore, such DPPs satisfy anarea law\documentclass[12pt]{minimal}
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				\begin{document}$$S\left( {\mathcal {X}}_{g} \mathcal {(}\Omega \mathcal {)}\right) \lesssim \left| \partial {\Omega } \right| $$\end{document}SXg(Ω)≲∂Ω, where\documentclass[12pt]{minimal}
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				\begin{document}$$\partial {\Omega }$$\end{document}∂Ωis the boundary of\documentclass[12pt]{minimal}
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				\begin{document}$$\Omega $$\end{document}Ωif they are ofClass I hyperuniformity(\documentclass[12pt]{minimal}
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				\begin{document}$${\mathbb {V}}\left( {\mathcal {X}} (\Omega )\right) \lesssim \left| \partial {\Omega }\right| $$\end{document}VX(Ω)≲∂Ω), while thearea law is violatedif they are ofClass II hyperuniformity(as\documentclass[12pt]{minimal}
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				\begin{document}$$\ L\rightarrow \infty $$\end{document}L→∞,\documentclass[12pt]{minimal}
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				\begin{document}$${\mathbb {V}}\left( {\mathcal {X}} (L\Omega )\right) \sim C_{\Omega }L^{d-1}\log L$$\end{document}VX(LΩ)∼CΩLd-1logL). As a result, the entanglement entropy of Weyl–Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.