Unidimensional Continuous-variable Quantum Key Distribution Research Articles

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.

Performance improvement of unidimensional continuous-variable quantum key distribution using zero-photon quantum catalysis

Compared with symmetric Gaussian-modulated coherent state protocol, the unidimensional continuous-variable quantum key distribution (UCVQKD) only modulates one of the quadratures in phase space of coherent state, thereby simplifying its implementation. Although UCVQKD does reduce the system’s complexity, its performance is reduced. In this work, we suggest an improved approach for UCVQKD using zero-photon quantum catalysis (ZPQC) technology. By taking advantage of this non-Gaussian operation, both secret key rate and maximal transmission distance of UCVQKD can be enhanced. Moreover, compared with another well-studied non-Gaussian operation, i.e., photon subtraction, ZPQC has higher success possibility, so that it would be beneficial for improving the amount of information acquired by legitimate users. Numerical simulation shows that the performance of UCVQKD can be improved by properly applying ZPQC. In particular, we find out that the performance of ZPQC-based UCVQKD outperforms that of photon subtraction-based UCVQKD, thereby providing an alternative way to better improve UCVQKD system. Furthermore, by taking finite-size effect into account, we derive more practical secure bound of ZPQC-based UCVQKD.

Enhancing the Unidimensional Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction

Unidimensional continuous-variable quantum key distribution (CV-QKD) protocol with Gaussian modulation is simpler in implementation and lower in costs than its two-dimensional counterpart, but its secure transmission distance is not as far as the latter. In this paper, we give a solution that using the photon subtraction, which is one of non-Gaussian operations, to improve the performance of the unidimensional CV-QKD protocol. Security analysis and numerical simulation indicate that the photon subtraction operation can significantly improve the secure transmission distance of the unidimensional CV-QKD protocol.

Atmospheric effect study of continuous-variable quantum key distribution.

We proposed a data acquisition method to monitor local oscillator (LO) intensity in real time in unidimensional continuous-variable quantum key distribution protocol. Based on this proposed method, the influence of weather conditions on the average transmittance and excess noise is studied, such as relative wetness, visibility, and beam jitter.

Unidimensional Continuous-variable Quantum Key Distribution Based on Basis-encoding Coherent States Protocol

We propose the unidimensional continuous-variable quantum key distribution(UDCVQKD) protocol based on the basis-encoding of Gaussian modulated coherent states. the UDCVQKD protocol disregards the necessity in one of the quadrature modulations in coherent states. On that basis, we propose our scheme by encoding the secret keys on the either randomly selected measurement bases: the phase quadrature (X) or the amplitude quadrature (P), in order to slightly weaken the effects of reconciliation efficiency and channel excess noise compare to the present UCVQKD protocol. The new protocol with a view to simplify the precedent unidimensional protocols in the decoding procedure, meanwhile ensure the security of the quantum communication.

Unidimensional continuous-variable quantum key distribution with noisy source

We investigate the security of unidimensional continuous-variable quantum key distribution with source noise at the sender. The source noise is ascribed to the legitimate sides rather than the eavesdropper and modeled as a thermal noise coupled with the signal mode through a beam splitter. The physicality bound and expressions of secret key rate are derived against collective entangling cloner attacks. Simulation results show that with source noise, the security bound of unidimensional protocol can be tightened. Moreover, proper source noise enlarges the security region to a wider range of parameters, thus eliminates potential eavesdropping threats and enhances the feasibility of unidimensional protocol.

Unidimensional Continuous-Variable Quantum Key Distribution with Untrusted Detection under Realistic Conditions

A unidimensional continuous-variable quantum key distribution protocol with untrusted detection is proposed, where the two legitimate partners send unidimensional modulated or Gaussian-modulated coherent states to an untrusted third party, i.e., Charlie, to realize the measurement. Compared with the Gaussian-modulated coherent-state protocols, the unidimensional modulated protocols take the advantage of easy modulation, low cost, and only a small number of random numbers required. Security analysis shows that the proposed protocol cannot just defend all detectors side channels, but also achieve great performance under certain conditions. Specifically, three cases are discussed in detail, including using unidimensional modulated coherent states in Alice’s side, in Bob’s side, and in both sides under realistic conditions, respectively. Under the three conditions, we derive the expressions of the secret key rate and give the optimal gain parameters. It is found that the optimal performance of the protocol is achieved by using unidimensional modulated coherent states in both Alice’s and Bob’s side. The resulting protocol shows the potential for long-distance secure communication using the unidimensional quantum key distribution protocol with simple modulation method and untrusted detection under realistic conditions.

Improvement of unidimensional continuous-variable quantum key distribution systems by using a phase-sensitive amplifier

Inherent defects of the detectors in a practical system cause deterioration of the performance of the unidimensional coherent-state continuous-variable quantum key distribution protocol. Aiming to achieve optimal performance, we propose a method of using a phase-sensitive amplifier to overcome the limitation that the detectors introduce. The modified protocol, corresponding to a higher key rate, provides the practical system with more robustness. To conduct a thorough investigation into the effects that the phase-sensitive amplifier creates, the expressions of the secret key rates are derived, under the conditions of coherent states, homodyne detection against collective attacks, and a phase-sensitive optical amplifier added at the output of the channel. Then, we carry out simulations to observe the performance in the cases of different gains. The simulation results demonstrate that the method we propose can improve the performance of the unidimensional protocol using coherent states and make up for the imperfections of the detector in a practical system.

Performance improvement of unidimensional continuous-variable quantum key distribution using heralded hybrid linear amplifier

We propose an improved scheme for unidimensional continuous-variable quantum key distribution (UCVQKD) using heralded hybrid linear amplifier, aiming to simplify the implementation and improve secret key rate. Different from the symmetrical continuous-variable quantum key distribution protocol (CVQKD), this scheme modulates one quadrature of the coherent state with security insurance. The heralded hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can tune between the high-gain or high noise-reduction for performance enhancement. Security analysis shows that the proposed scheme can be secured under the collective attacks. Compared with traditional UCVQKD involving noiseless amplifier, the security transmission distance of proposed protocol is increased by 24 kilometers. It not only simplifies the modulation process but also has approximate performance with symmetrical CVQKD in terms of maximal security transmission distance.

Unidimensional continuous-variable quantum key distribution with discrete modulation

In this paper, we proposed an unidimensional continuous-variable quantum key distribution (CV-QKD) protocol with discrete modulation, which waives the necessity in one of the quadrature modulations and further simplified the implementation of the CV-QKD protocol. On the basis of the Heisenberg uncertainty relation, we analyze the boundary between the unphysical and physical region. Besides, we utilize a novel proof approach to achieve a lower bound valid of transmission distance. This scheme shows an available method to further simplified the implementation of the QKD.

Unidimensional continuous-variable quantum key distribution using squeezed states

The possibility of using squeezed states in the recently suggested unidimensional continuous-variable quantum key distribution based on a single quadrature modulation is addressed. It is shown that squeezing of the signal states expands the physicality bounds of the effective entangled state shared between the trusted parties due to the antisqueezing noise in the unmodulated quadrature. Modulation of the antisqueezed quadrature, on the other hand, effectively shrinks the physicality bounds due to the squeezing in the unmodulated quadrature and also provides noise on the reference side of the protocol, thus limiting the possibility of eavesdropping in noisy channels. This strategy is practical for low-loss (i.e., short-distance) channels, especially if direct reconciliation scheme is applied.

Composable security of unidimensional continuous-variable quantum key distribution

We investigate the composable security of unidimensional contin- uous variable quantum key distribution (UCVQKD), which is based on the Gaussian modulation of a single quadrature of the coherent-state of light, aiming to provide a simple implementation of key distribution compared to the symmetrically modulated Gaussian coherent-state protocols. This protocol neglects the necessity in one of the quadrature modulation in coherent-states and hence reduces the system complexity. To clarify the influence of finite-size effect and the cost of performance degeneration, we establish the relation- ship of the balanced parameters of the unmodulated quadrature and estimate the precise secure region. Subsequently, we illustrate the composable security of the UCVQKD protocol against collective attacks and achieve the tightest bound of the UCVQKD protocol. Numerical simulations show the asymptotic secret key rate of the UCVQKD protocol, together with the symmetrically modulated Gaussian coherent-state protocols.

Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations

We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol.

Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions

We analyze the unidimensional (UD) continuous-variable quantum key distribution protocol in a finite size scenario under realistic conditions. The dependence of the secret key rate on realistic parameters is analyzed numerically. A method of calculating the optimal ratio to divide the data samples in order to achieve the largest secret key rate is proposed. When the data samples are large, the superiority of the UD protocol in data processing becomes apparent. It is expected that the features and methods presented in this paper will aid in the exploration of the latent capacity of the UD protocol as well as the development of further applications.

Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution

We experimentally demonstrated an all-fiber-based unidimensional continuous-variable quantum key distribution (CV QKD) protocol and analyzed its security under collective attack in realistic conditions. A pulsed balanced homodyne detector, which could not be accessed by eavesdroppers, with phase-insensitive efficiency and electronic noise, was considered. Furthermore, a modulation method and an improved relative phase-locking technique with one amplitude modulator and one phase modulator were designed. The relative phase could be locked precisely with a standard deviation of 0.5\ifmmode^\circ\else\textdegree\fi{} and a mean of almost zero. Secret key bit rates of 5.4 kbps and 700 bps were achieved for transmission fiber lengths of 30 and 50 km, respectively. The protocol, which simplified the CV QKD system and reduced the cost, displayed a performance comparable to that of a symmetrical counterpart under realistic conditions. It is expected that the developed protocol can facilitate the practical application of the CV QKD.

Unidimensional continuous-variable quantum key distribution

We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in phase quadrature modulation and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channels is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.