Heisenberg-limited eavesdropping on the continuous-variable quantum cryptographic protocol with no basis switching is impossible

The Gaussian quantum key distribution protocol based on coherent states and heterodyne detection [Phys. Rev. Lett. 93, 170504 (2004)] has the advantage that no active random basis switching is needed on the receiver's side. Its security is, however, not very satisfyingly understood today because the bounds on the secret key rate that have been derived from Heisenberg relations are not attained by any known scheme. Here, we address the problem of the optimal Gaussian individual attack against this protocol, and derive tight upper bounds on the information accessible to an eavesdropper. The optical scheme achieving this bound is also exhibited, which concludes the security analysis of this protocol.