(B)         10,626 (80 kb)                                                                          
            $2048^3$            33                0.1               $\pi/4$    $8.6\times 10^9$ (64 Gb)    (A)    825,922 (6.6 Mb)  
   “ & 33 & 0.1 & $\pi/4$ & ”   (B)        156,720 (1.22 Mb)                                                                        

  : Summary of resources to describe numerically the Gaussian probability distributions with covariance matrices given by  and , using $m$ qubits per dimension, either in an exact form—storing all values $p^{(m)}(x_s)$—or in the compact MPS representation .[]{data-label="tab:state-sizes"}

The output of these simulations is shown in Fig. \[fig:entropies\]. When $\theta=0,$ the wavefunction $\ket{p^{(m)}_{2d}}$ is a product state $\ket{p^{(m)}(\sigma_{max})}\otimes\ket{p^{(m)}(\sigma_{min})}$ of two one-dimensional distributions. As shown in Fig. \[fig:entropies\]b (blue solid), the maximum entanglement over all one-dimensional bipartitions is less than one e-bit, consistent with Sect. \[sec:numerics-1d\]. To grow the entanglement we must combine squeezing and rotation, recreating a two-mode squeezed state. From the theory of Gaussian states, the entanglement should be maximal for $\theta=\pi/4$ and it should diverge with the squeezing. Our simulations confirm this prediction for the (A) order. Fig. \[fig:entropies2d\]b (orange, solid) shows that the maximum bipartite entanglement between our qubit variables grows as $(\sigma_\text{max}/\sigma_\text{min}){1/4}.$ This entanglement is also spread all along the chain of qubits, as seen in Fig. \[fig:entropies2d\]c. We can even improve on these results. As shown in 