We address the effect of classical correlations, introduced to a quantum resource used for the continuous-variable quantum key distribution. The set-up is based on an entangled source with two trusted parties performing homodyne measurements on their modes, thus corresponding to the preparation of squeezed states, while one of the modes is traveling to the remote party through lossy and noisy channel. The security of the scheme is considered against individual and collective eavesdropping attacks. It is shown that the classical correlations added to the entangled source increase the performance of the scheme both quantatively in terms of the secure key rate and qualitatively in terms of the security region with respect to the tolerable excess noise for both types of attacks and the improvement is essentially significant for sources possessing low degree of nonclassicality.
We address the effect of classical correlations, introduced to a quantum resource used for the continuous-variable quantum key distribution. The set-up is based on an entangled source with two trusted parties performing homodyne measurements on their modes, thus corresponding to the preparation of squeezed states, while one of the modes is traveling to the remote party through lossy and noisy channel. The security of the scheme is considered against individual and collective eavesdropping attacks. It is shown that the classical correlations added to the entangled source increase the performance of the scheme both quantatively in terms of the secure key rate and qualitatively in terms of the security region with respect to the tolerable excess noise for both types of attacks and the improvement is essentially significant for sources possessing low degree of nonclassicality.
We propose an improved two-way continuous-variable quantum key distribution (CV QKD) protocol by adding proper random noise on the receiver's homodyne detection, the security of which is analysed against general collective attacks. The simulation result under the collective entangling cloner attack indicates that despite the correlation between two-way channels decreasing the secret key rate relative to the uncorrelated channels slightly, the performance of the two-way protocol is still far beyond that of the one-way protocols. Importantly, the added noise in detection is beneficial for the secret key rate and the tolerable excess noise of this two-way protocol. With the reasonable reconciliation efficiency of 90%, the two-way CV QKD with added noise allows the distribution of secret keys over 60 km fibre distance.
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 consider the security of continuous-variable quantum key distribution using thermal (or noisy) Gaussian resource states. Specifically, we analyze this against collective Gaussian attacks using direct and reverse reconciliation where both protocols use either homodyne or heterodyne detection. We show that in the case of direct reconciliation with heterodyne detection, an improved robustness to channel noise is achieved when large amounts of preparation noise is added, as compared to the case when no preparation noise is added. We also consider the theoretical limit of infinite preparation noise and show a secure key can still be achieved in this limit provided the channel noise is less than the preparation noise. Finally, we consider the security of quantum key distribution at various electromagnetic wavelengths and derive an upper bound related to an entanglement-breaking eavesdropping attack and discuss the feasibility of microwave quantum key distribution.
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.
Quantum key distribution (QKD) protocols allow two trusted parties to distribute a cryptographic key which they can further use for the unconditionally secure classical communication. During the last decades the field has grown mature with the commercial prototypes being available. They mostly rely on the faint laser pulses implementing the protocols on the basis of single qubits and qubit pairs. Alternatively, the continuous-variable (CV) protocols based on the multi-photon states of light were developed recently. They are typically built using the quadrature modulation of the coherent or squeezed states and subsequent homodyne detection. In the case of Gaussian modulation the security of the protocols is based on the extremality of Gaussian states, which allows estimating bounds on the leaked information. The Gaussian CV QKD protocols were shown secure for any degree of channel attenuation, but are restricted by the channel noise. Moreover, the applicability of Gaussian CV QKD protocols is limited by the effectiveness of classical post-processing algorithms, used by the trusted parties to process the measured data and distill the cryptographic key. On the other hand, the squeezedstate CV QKD protocols were previously considered ineffective under limited degrees of squeezing, while strong squeezing remains experimentally challenging. In the present work we distinguish between the classical and quantum resources in the Gaussian CV QKD and address the role of nonclassicality in the Gaussian protocols. We demonstrate, that by properly combining squeezed resource and coherent modulation, trusted parties are able to decouple eavesdropper from the channel, thus being able to establish the secure key from any amount of the classical mutual information. Our result shows a very promising path towards the long-distance CV QKD.
We address the applicability of the continuous-variables quantum key distribution in the realistic conditions of noisy preparation, channel loss and detection noise and investigate the possibility to increase its tolerance to the state preparation noise. The two types of preparation noise, either phase-sensitive or phase-insensitive excess noise, are considered in the assumption of optimal attacks performed by an eavesdropper within the setup based on the entangled source and either homodyne or heterodyne measurements. We show that preparation noise is destructive for the secure channel upon even low noise variances in the conditions of channel loss, while detection noise just decreases the key rate. We propose the method of sender-side attenuation to suppress the preparation noise in the entanglements-based scheme and show that it enables the secure key transmission upon arbitrary high preparation noise of both types and any pure channel loss against both individual and collective attacks.