GG02. The difference is that the postselection, performed along the quadrature axes, introduces some privileged directions in phase space. Consequently one needs to actively symmetrize the protocol to make it invariant under rotations in phase space.

Conclusion
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In this paper, we provided a first step towards a general security proof of CVQKD protocols with postselection. Until now, its security was only established in the very restricted case of Gaussian attacks, which are very unlikely to be optimal. Thanks to an active symmetrization of the protocol (performed on the classical data of Alice and Bob), one can show that collective attacks and actually arbitrary attacks in the asymptotic limit basically reduce to Gaussian attacks. The present solution is still not very practical since one would need to randomly sample from the unitary group in a very large dimension. Two possible approaches should be considered: either looking at a much smaller set of transformations for which the sampling can be performed efficiently, or improving the bounds derived here, possibly combining the symmetrization technique with some de Finetti-type arguments. It seems almost clear, at any rate, that the symmetrization technique introduced here will be required for any further advance in the study 