Role of anti-squeezing noise in continuous-variable quantum cryptography

Quadrature squeezing is known to enforce continuous-variable quantum cryptography. However, in practice, squeezed states are never generated perfectly and always contain anti-squeezing quadrature noise concerned with losses in the optical parametric oscillator sources. We therefore address the role of anti-squeezing noise in continuous-variable quantum cryptography over attenuating and noisy quantum channels. We first assume that anti-squeezing noise is trusted, hence, out of control of a potential eavesdropper, capable of collective attacks. In this regime, anti-squeezing noise can be even helpful by tightening the bound on the information leakage in the quantum channel. Moreover, in the asymptotic limit of infinitely strong trusted anti-squeezing noise, the bound can be expressed analytically. We then assume that anti-squeezing noise is controlled by an eavesdropper, thus being a side-channel in the source implementation. In this regime, the anti-squeezing noise leads to the security break both in direct and reverse reconciliation scenarios. We compare the bounds on the untrusted phase-sensitive anti-squeezing noise to the typical phase-insensitive channel excess noise and show that protocols are more robust to the anti-squeezing noise, while the presence of such noise makes the protocol more sensitive to the noise in the main quantum channel. The obtained results reveal the important role of anti-squeezing noise in continuous-variable quantum cryptography and suggest the need of pure squeezed state preparation in the case of untrusted sources.