Fig. \[fig:states\]d shows the maximum entanglement entropy over all bipartitions as we change the parameter $\sigma.$ The first three probability distributions have a bounded entanglement below an e-bit. The non-log-convex distribution $p_{nc}(x)$ behaves slightly different: increasing $\sigma$ leads to the appearance of more peaks, that are more difficult to describe. This causes a steady increase in entropy, but this is slow enough that still facilitates an efficient construct.

Extensions to more variables {#sec:numerics-2d}
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Challenging applications to fields such as Physics, fluid dynamics or finance [@orus2019] require the study of states with many more, $p(x_1,x_2\ldots).$ To better understand the scaling of entanglement and the complexity of the state, we have studied the discretization  of two- and three-dimensional Gaussian distributions $$\label{eq:Gaussian-nd}
  p(\vec{x}) = \frac{1}{(2\pi)^{N/2}\mathrm{det}(\Sigma)}\exp\left(-\frac{1}{2}\vec{x}^T\Sigma^{-2}\vec{x}\right),\;\vec{x}\in\mathbb{R}^N,$$ with covariance matrix $\Sigma$ and zero mean, using the same number of qubits in all dimensions.

As in the 1D problem, we will treat the quantum register as a one-dimensional arrangement of qubits, studying the entanglement over all 1D bipartitions. Naturally, the complexity of this discretization will depend on how we arrange the qubits. The simple straightforward order (A) distributes the qubits sequentially, first by coordinate, then by significance. In this order, Gaussian states with a diagonal 