The role of the side channels in the continuous-variable quantum key distribution is studied. It is shown how the information leakage through a side channel from the trusted sender station increases the vulnerability of the protocols to the eavesdropping in the main quantum communication channel. Moreover, the untrusted noise infusion by an eavesdropper on the trusted receiving side breaks the security even for a purely attenuating main quantum channel. As a method to compensate for the effect of the side-channel leakage on the sender side, we suggest several types of manipulations on the side-channel input. It is shown that by applying the modulated coherent light on the input of the side channel that is optimally correlated to the modulation on the main signal and optionally introducing additional squeezing in the case of the squeezed-state protocol, the negative influence of the lossy side channel on the sender side can be completely removed. For the trusted receiving side, the method of optimal monitoring of the residual noise from the side-channel noise infusion is suggested and shown to be able to completely eliminate the presence of the noisy side channel. We therefore prove that the side-channel effects can be completely removed using feasible operations if the trusted parties access the respective parts of the side channels.
The role of the side channels in the continuous-variable quantum key distribution is studied. It is shown how the information leakage through a side channel from the trusted sender station increases the vulnerability of the protocols to the eavesdropping in the main quantum communication channel. Moreover, the untrusted noise infusion by an eavesdropper on the trusted receiving side breaks the security even for a purely attenuating main quantum channel. As a method to compensate for the effect of the side-channel leakage on the sender side, we suggest several types of manipulations on the side-channel input. It is shown that by applying the modulated coherent light on the input of the side channel that is optimally correlated to the modulation on the main signal and optionally introducing additional squeezing in the case of the squeezed-state protocol, the negative influence of the lossy side channel on the sender side can be completely removed. For the trusted receiving side, the method of optimal monitoring of the residual noise from the side-channel noise infusion is suggested and shown to be able to completely eliminate the presence of the noisy side channel. We therefore prove that the side-channel effects can be completely removed using feasible operations if the trusted parties access the respective parts of the side channels.
We address side-channel leakage in a trusted preparation station of continuous-variable quantum key distribution with coherent and squeezed states. We consider two different scenarios: multimode Gaussian modulation, directly accessible to an eavesdropper, or side-channel loss of the signal states prior to the modulation stage. We show the negative impact of excessive modulation on both the coherent- and squeezed-state protocols. The impact is more pronounced for squeezed-state protocols and may require optimization of squeezing in the case of noisy quantum channels. Further, we demonstrate that the coherent-state protocol is immune to side-channel signal state leakage prior to modulation, while the squeezed-state protocol is vulnerable to such attacks, becoming more sensitive to the noise in the channel. In the general case of noisy quantum channels the signal squeezing can be optimized to provide best performance of the protocol in the presence of side-channel leakage prior to modulation. Our results demonstrate that leakage from the trusted source in continuous-variable quantum key distribution should not be underestimated and squeezing optimization is needed to overcome coherent state protocols.
We address the problem of the security of the continuous variable quantum key distribution with the coherent states in the presence of a trusted noise of different origins, e.g. preparation noise at the sender side and the detection noise at the remote receiver side. We show the essential difference between the impact of these types of noise under conditions of lossy quantum channel, available to an eavesdropper. While detection noise reduces the key rate without breaking the security, the preparation noise is destructive for the secure transmission. At the same time we show that by the state purification we can compensate for the destructive effect of the preparation noise, so that upon optimal purification its impact becomes similar to that of the detection noise. The effect is persistent also upon realistic error correction.
We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.
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.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.