collective attacks [@GC06; @NGA06; @PBL08]. Using de Finetti theorem and conditioned upon an extra verification step [@RC09], these collective attacks are actually optimal in general in the asymptotic limit. The only step which is currently missing in this security analysis is a tight reduction from coherent to collective attacks in the finite-size regime [@LGG10].

The security status of other CVQKD protocols is far less advanced. In particular, not much is known for protocols using postselection [@SRL02; @LKL04; @LSS05]. In these protocols, the idea is that Alice and Bob will only use some data to distill the secret key and discard the rest. More precisely, they only keep the data compatible with a positive key rate. This method, inspired by advantage distillation techniques, certainly makes the protocol more robust against imperfections such as losses or noise in the channel, and potentially gives the best practical CVQKD protocol (see Refs. [@LSS05; @LRH06] for experimental implementations). It is therefore of considerable importance to be able to assess its security. Unfortunately, there are currently no full security proof for this scheme, not even against collective attacks. In fact, the only result available so far is an analysis in the case of Gaussian attacks [@HL07; 