Fig. \[fig:entropies2d\]b, if we adopt the renormalization order (B), all states can be described with $N=2$ e-bits of entanglement. Moreover, the entanglement distribution concentrates around the most significant qubits \[cf. Fig. \[fig:entropies2d\]c (dashed, green)\], producing significantly smaller tensors.

Despite the growth of entanglement, the quantum states that we create always admit a compact MPS representation that beats the classical approach of storing the full wavefunction. As shown in Table \[tab:state-sizes\], a highly-correlated discretization in the (A) order with 14 and 18 bits per coordinate, requires 1Mb of floating point real numbers in MPS form. The same states stored using the (B) order, take, in the worst scenario $\sigma_{min}=0.1\sigma_{max}$ with $\theta=\pi/4,$ just about 80 kilobytes of information. All this is to be compared to the 2 Gb and 524 Tb of data required to write down the wavefunctions of $28$ and $36$ qubits.

![(a) Maximum entanglement over all bipartitions for a three-dimensional Gaussian state , computed with exact wavefunctions ($m=7$ bits per mode, lines) or MPS ($m=9$ bits per mode, circles), using different squeezing rates, angles and orders. (b) Illustration of the three-dimensional Gaussian probability distribution for $\sigma_{min}=0.5\sigma_{max}.$[]{data-label="fig:entropies3d"}](fig-entropies3d.pdf){width="0.75\linewidth"}

We have performed the same study using three-dimensional Gaussian states. For concreteness, we 