Two-way Continuous-variable Quantum Key Distribution Research Articles

Security of plug-and-play continuous-variable quantum key distribution

Subject of study. Two-way continuous-variable quantum key distribution schemes are studied. Aim. This study aims to prove the security of the plug-and-play continuous-variable quantum key distribution system in the context of the model of trusted noise from legitimate users. Method. Based on an analog of the well-known implementation in the plug-and-play format, the performance of such a system operating under the GG02 protocol is evaluated. The evaluation is conducted in the presence of collective attacks, considering the finite-key effects. Main results. A secure key that satisfies the composability criteria can be distributed with a channel loss of 5 dB, which is expected to be approximately half that in a one-way scheme. Practical significance. Two-way quantum key distribution schemes are more stable than one-way schemes, and hence, their stability requires detailed consideration. This paper is the first, to our knowledge, to propose considering the security of a two-way implementation of continuous-variable quantum key distribution, considering the trusted equipment noise.

Unidimensional Two-Way Continuous-Variable Quantum Key Distribution Using Coherent States.

We propose a unidimensional two-way continuous-variable quantum key distribution protocol with coherent states, where the sender modulates a single quadrature of the coherent states rather than both quadratures to simplify the structure of a two-way system. Security analysis is performed with a general attack strategy, known as two-mode attack, which helps to reduce limitations in the analysis. The performance of the protocol under all accessible two-mode attacks at fixed distance is illustrated. Further, two typical two-mode attack strategies are obtained from it, which are one-mode attack strategy and optimal two-mode attack strategy. Between them, the one-mode attack is the simplest form of the two-mode attack, while the optimal two-mode attack is the most complicated one. Simulations show that though the system is simplified, the performance of the two-way protocol with unidimensional modulation is still comparable to that of the counterpart with Gaussian modulation even against the optimal two-mode attack when Eve’s ability is maximized. Thus, the proposed protocol simplifies the two-way system while guaranteeing its performance to a certain extent. Especially in a practical system with short transmission distance and high excess noise, the protocol has a good application prospect.

Composable security of two-way continuous-variable quantum key distribution without active symmetrization

We present a general framework encompassing a number of continuous-variable quantum key distribution protocols, including standard one-way protocols, measurement-device-independent protocols as well as some two-way protocols, or any other continuous-variable protocol involving only a Gaussian modulation of coherent states and heterodyne detection. The main interest of this framework is that the corresponding protocols are all covariant with respect to the action of the unitary group $U(n)$, implying that their security can be established thanks to a Gaussian de Finetti reduction. In particular, we give a composable security proof of two-way continuous-variable quantum key distribution against general attacks. We also prove that no active symmetrization procedure is required for these protocols, which would otherwise make them prohibitively costly to implement.

Improvement of two-way continuous-variable quantum key distribution with virtual photon subtraction

We propose a method to improve the performance of two-way continuous-variable quantum key distribution protocol by virtual photon subtraction. The Virtual photon subtraction implemented via non-Gaussian post-selection not only enhances the entanglement of two-mode squeezed vacuum state but also has advantages in simplifying physical operation and promoting efficiency. In two-way protocol, virtual photon subtraction could be applied on two sources independently. Numerical simulations show that the optimal performance of renovated two-way protocol is obtained with photon subtraction only used by Alice. The transmission distance and tolerable excess noise are improved by using the virtual photon subtraction with appropriate parameters. Moreover, the tolerable excess noise maintains a high value with the increase of distance so that the robustness of two-way continuous-variable quantum key distribution system is significantly improved, especially at long transmission distance.

Numerical simulation of the optimal two-mode attacks for two-way continuous-variable quantum cryptography in reverse reconciliation

We analyze the security of the two-way continuous-variable quantum key distribution protocol in reverse reconciliation against general two-mode attacks, which represent all accessible attacks at fixed channel parameters. Rather than against one specific attack model, the expression of secret key rates of the two-way protocol are derived against all accessible attack models. It is found that there is an optimal two-mode attack to minimize the performance of the protocol in terms of both secret key rates and maximal transmission distances. We identify the optimal two-mode attack, give the specific attack model of the optimal two-mode attack and show the performance of the two-way protocol against the optimal two-mode attack. Even under the optimal two-mode attack, the performances of two-way protocol are still better than the corresponding one-way protocol, which shows the advantage of making double use of the quantum channel and the potential of long-distance secure communication using a two-way protocol.

Quantum hacking of two-way continuous-variable quantum key distribution using Trojan-horse attack**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the National Natural Science Foundation of China (Grant Nos. 11304397 and 61505261).

We present a Trojan-horse attack on the practical two-way continuous-variable quantum key distribution system. Our attack mainly focuses on the imperfection of the practical system that the modulator has a redundancy of modulation pulse-width, which leaves a loophole for the eavesdropper inserting a Trojan-horse pulse. Utilizing the unique characteristics of two-way continuous-variable quantum key distribution that Alice only takes modulation operation on the received mode without any measurement, this attack allows the eavesdropper to render all of the final keys shared between the legitimate parties insecure without being detected. After analyzing the feasibility of the attack, the corresponding countermeasures are put forward.

General immunity and superadditivity of two-way Gaussian quantum cryptography.

We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.

Performance Improvement of Two-way Quantum Key Distribution by Using a Heralded Noiseless Amplifier

We show the successful use of a heralded noiseless linear amplifier on the detection stage in the two-way continuous-variable quantum key distribution to improve the performance. Due to the excess noise, the secret-key rate of the two-way protocol becomes negative for a certain distance of transmission. The use of a heralded noiseless linear amplifier increases this distance by the equivalent of 20 log10g dB of losses, and it also helps the two-way protocol tolerate more excess noise.

Security of two-way continuous-variable quantum key distribution with source noise

We investigate the security of reverse reconciliation two-way continuous-variable quantum key distribution with source noise at both legitimate sides. Because the source noise originates from imperfect devices, we ascribe it to the legitimate sides rather than the eavesdropper. The trusted model consists of a thermal noise injected into a beam splitter. The expressions of secret key rate are derived against collective entangling cloner attacks for homodyne and heterodyne detections. Simulation results show that by applying the trusted model, the security bound of the reverse reconciliation two-way protocols can be tightened, while the advantage over one-way protocols still maintains.

Improvement of two-way continuous-variable quantum key distribution using optical amplifiers

The imperfections of a receiver's detector affect the performance of two-way continuous-variable (CV) quantum key distribution (QKD) protocols and are difficult to adjust in practical situations. We propose a method to improve the performance of two-way CV-QKD by adding a parameter-adjustable optical amplifier at the receiver. A security analysis is derived against a two-mode collective entangling cloner attack. Our simulations show that the proposed method can improve the performance of protocols as long as the inherent noise of the amplifier is lower than a critical value, defined as the tolerable amplifier noise. Furthermore, the optimal performance can approach the scenario where a perfect detector is used.

An improved two-way continuous-variable quantum key distribution protocol with added noise in homodyne detection

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.

SECURITY OF A NEW TWO-WAY CONTINUOUS-VARIABLE QUANTUM KEY DISTRIBUTION PROTOCOL

The original two-way continuous-variable quantum-key-distribution (CV-QKD) protocols [S. Pirandola, S. Mancini, S. Lloyd and S. L. Braunstein, Nat. Phys. 4 (2008) 726] give the security against the collective attack on the condition of the tomography of the quantum channels. We propose a family of new two-way CV-QKD protocols and prove their security against collective entangling cloner attacks without the tomography of the quantum channels. The simulation result indicates that the new protocols maintain the same advantage as the original two-way protocols whose tolerable excess noise surpasses that of the one-way CV-QKD protocol. We also show that all sub-protocols within the family have higher secret key rate and much longer transmission distance than the one-way CV-QKD protocol for the noisy channel.