We address the security of continuous-variable quantum key distribution with squeezed states upon the realistic conditions of noisy and lossy environment and limited reconciliation efficiency. Considering the generalized preparation scheme and clearly distinguishing between classical and quantum resources, we investigate the effect of finite squeezing on the tolerance of the protocol to untrusted channel noise. For a long-distance strongly attenuating channel and the consequent low reconciliation efficiency, we show that feasible limited squeezing is surprisingly sufficient to provide the security of Gaussian quantum key distribution in the presence of untrusted noise. We explain the effect by the behaviour of the Holevo quantity, which describes the information leakage and is effectively minimized by the squeezed states.
We address the security of continuous-variable quantum key distribution with squeezed states upon the realistic conditions of noisy and lossy environment and limited reconciliation efficiency. Considering the generalized preparation scheme and clearly distinguishing between classical and quantum resources, we investigate the effect of finite squeezing on the tolerance of the protocol to untrusted channel noise. For a long-distance strongly attenuating channel and the consequent low reconciliation efficiency, we show that feasible limited squeezing is surprisingly sufficient to provide the security of Gaussian quantum key distribution in the presence of untrusted noise. We explain the effect by the behaviour of the Holevo quantity, which describes the information leakage and is effectively minimized by the squeezed states.
We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.
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.
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.
In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.
Abstract In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.