Phase Estimation and Compensation for Continuous-Variable Quantum Key Distribution

Phase estimation and compensation is one of the enabling functionalities in continous-variable quantum key distribution (CVQKD). Recently, a novel CVQKD scheme has been independently proposed to combat the local oscillator (LO) side channel attacks. Furthermore, we have carried out a proof-of-principle experimental study on the feasibility of the CVQKD without sending a LO. However, this scheme contains a serious weakness: The phase noise caused by the two different lasers between the sender and the receiver would severely destroy the quantum signal and finally reduce the secure distance. In this paper, we investigate the optical phase noise and explore the optimal approach to estimate and compensate such kind of noise with appropriate data overhead. Numerical simulations show that our scheme can successfully reconstruct the phase drifts even at low signal-to-noise ratio conditions. We also suggest that a higher accuracy of phase estimation could be achieved by using the frequency division multiplexing scheme. This opens an opportunity to employ advanced pilot-aided phase estimation techniques in quantum communication system.

     

Multi-mode Gaussian Modulated Continuous-Variable Measurement-Device-Independent Quantum Key Distribution

We propose a novel multi-mode Gaussian modulated continuous variable measurement-device-independent quantum key distribution (MDI-CVQKD) protocol where Alice and Bob prepare independent and identically distributed Gaussian modulated coherent states in multiple independent modes respectively along with Charlie using a traditional noise homodyne detector to measure. Since it is completely handed over to an untrusted third party (Charlie) to measure, this protocol can effectively eliminate the defects of the actual detector. As well as, we also proved that the multi-mode MDI-CVQKD protocol can reduce electronic noise. The simulation results show that the multi-mode Gaussian modulated MDI-CVQKD protocol can indeed significantly improve the key rate of the original Gaussian modulated MDI-CVQKD protocol, and extend the maximum secure transmission distance of the secret key.

     

Subcarrier Domain of Multicarrier Continuous-Variable Quantum Key Distribution

Journal of Statistical Physics - The subcarrier domain of multicarrier continuous-variable quantum key distribution (CVQKD) is defined. In a multicarrier CVQKD scheme, the information is granulated...     

A Hierarchical Modulation Coherent Communication Scheme for Simultaneous Four-State Continuous-Variable Quantum Key Distribution and Classical Communication

We present a hierarchical modulation coherent communication protocol, which simultaneously achieves classical optical communication and continuous-variable quantum key distribution. Our hierarchical modulation scheme consists of a quadrature phase-shifting keying modulation for classical communication and a four-state discrete modulation for continuous-variable quantum key distribution. The simulation results based on practical parameters show that it is feasible to transmit both quantum information and classical information on a single carrier. We obtained a secure key rate of \(10^{-3}\) bits/pulse to \(10^{-1}\) bits/pulse within 40 kilometers, and in the meantime the maximum bit error rate for classical information is about \(10^{-7}\). Because continuous-variable quantum key distribution protocol is compatible with standard telecommunication technology, we think our hierarchical modulation scheme can be used to upgrade the digital communication systems to extend system function in the future.     

Four-State Continuous-Variable Quantum Key Distribution with Photon Subtraction

Four-state continuous-variable quantum key distribution (CVQKD) is one of the discretely modulated CVQKD which generates four nonorthogonal coherent states and exploits the sign of the measured quadrature of each state to encode information rather than uses the quadrature \(\hat {x}\) or \(\hat {p}\) itself. It has been proven that four-state CVQKD is more suitable than Gaussian modulated CVQKD in terms of transmission distance. In this paper, we propose an improved four-state CVQKD using an non-Gaussian operation, photon subtraction. A suitable photon-subtraction operation can be exploited to improve the maximal transmission of CVQKD in point-to-point quantum communication since it provides a method to enhance the performance of entanglement-based (EB) CVQKD. Photon subtraction not only can lengthen the maximal transmission distance by increasing the signal-to-noise rate but also can be easily implemented with existing technologies. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance. Furthermore, by taking finite-size effect into account we obtain a tighter bound of the secure distance, which is more practical than that obtained in the asymptotic limit.     

Source-Manipulating Wavelength-Dependent Continuous-Variable Quantum Key Distribution with Heterodyne Detectors

The intensities of signal and local oscillator (LO) can be elegantly manipulated for the noise-based quantum system while manipulating the wavelength-dependent modulation in source to increase the performance of the continuous-variable key distribution in terms of the secret key rate and maximal transmission distance. The source-based additional noises can be tuned and stabilized to the suitable values to eliminate the effect of the LO fluctuations and defeat the potential attacks in imperfect quantum channels. It is firmly proved that the secret key rate can be manipulated in source over imperfect channels by the intensities of signal and LO with different wavelengths, which have an effect on the optimal signal-to-noise ratio of the heterodyne detectors resulting from the detection efficiency and the additional electronic noise as well. Simulation results show that there is a nice balance between the secret key rate and the maximum transmission distance.     

Quantum Key Distribution Based on Coherent States

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Continuous-Variable Measurement-Device-Independent Quantum Key Distribution with One-Time Shot-Noise Unit Calibration

Imperfections in practical detectors,including limited detection efficiency,and inherent electronic noise,can seriously decrease the transmission distance of continuous-variable measurement-device-independent quantum key distribution systems.Owing to the difficulties inherent in realizing a high-efficiency fiber homodyne detector,challenges still exist in continuous-variable measurement-device-independent quantum key distribution system implementation.We offer an alternative approach in an attempt to solve these difficulties and improve the potential for system implementation.Here,a novel practical detector modeling method is utilized,which is combined with a one-time shot-noise-unit calibration method for the purpose of system realization.The new modeling method benefits greatly from taking advantage of one-time shot-noise-unit calibration methods,such as measuring electronic noise and shot noise directly to a novel shot-noise unit,so as to eliminate the statistical fluctuations found in previous methods;this makes the implementation of such systems simpler,and the calibration progress more accurate.We provide a simulation of the secret key rate versus distance with different parameters.In addition,the minimal detection efficiency required at each distance,as well as the contrast between the two methods,are also shown,so as to provide a reference in terms of system realization.     

Continuous-Variable Quantum Teleportation of Entangled Coherent States

We propose a quantum teleportation scheme for tripartite entangled coherent state （ECS） with continuous variable. Our scheme is feasible and economical in the sense that we need only linear optical devices such as beam splitters, phase shifters and photon detectors and employ three bipartite maximally ECSs as quantum channels. We also generalize the tripartite scheme into multipartite ease and calculate the minimum average fidelity for the schemes in tripartite and multipartite cases.     

Improving Continuous-Variable Quantum Key Distribution Using the Heralded Noiseless Linear Amplifier with Source in the Middle

We characterize the efficiency of the practical continuous-variable quantum key distribution (CVQKD) while inserting the heralded noiseless linear amplifier (NLA) before detectors to increase the secret key rate and the maximum transmission distance in Gaussian channels. In the heralded NLA-based CVQKD system, the entanglement source is only placed in the middle while the two participants are unnecessary to trust their source. The intensities of source noise are sensitive to the tunable NLA with the parameter g in a suitable range and can be stabilized to the suitable constant values to eliminate the impact of channel noise and defeat the potential attacks. Simulation results show that there is a well balance between the secret key rate and the maximum transmission distance with the tunable NLA.     

Continuous-Variable Quantum Key Distribution with Orthogonal Frequency Division Multiplexing Modulation

We demonstrate a multicarrier QKD protocol for continuous-variables (CV) using the orthogonal frequency division multiplexing (OFDM) technique which was employed in frequency domain. The multicarrier communication formulates sub-channels from OFDM technique and physical quantum channel, each dedicated to the transmission of a subcarrier CV. In the OFDM-CVQKD scenario, the input quantum states of the legal parties are granulated into subcarrier CVs, at the receiver, the subcarriers are decoded by an unitary CV operation, which results in the recovered single-carrier CVs. Compared with the device of the multichannel parallel CVQKD protocol that utilizes N arrayed-waveguide gratings (AWG) in optical domain, this protocol shows better feasibility of implementation from both equipment and technique. We derive the formulas of the secret key rate, moreover, analyze the security in the finite-size through the OFDM-CVQKD scheme. Simulation results indicate that the OFDM-CVQKD scheme leads to improved secret key rates and higher tolerable excess noise in comparison to single-carrier CVQKD. Particularly, the secret key rate of the 64 subcarrier CVQKD has increased by roughly an order of magnitude of the single-channel CVQKD, whereas the tolerable excess noise can be controlled in a small range. The results reveal that the OFDM-CVQKD protocol provides a feasible framework for the experimental implementation of an unconditionally secure communication over standard telecommunication networks.     

The Improvement of Performance for Continuous-Variable Quantum Key Distribution with Imperfect Gaussian Modulation

Gaussian modulation is one of the key steps for the implementation of continuous-variable quantum key distribution (CVQKD) schemes. However, imperfection in the Gaussian modulation may introduce modulation noise that can deteriorate the performance of CVQKD systems. In this paper, we mainly investigate how to improve the performance of a CVQKD system from different aspects. First, we explore the several different origins, impacts and monitoring schemes for the modulation noise in detail. Then, we discuss the practical performance of a CVQKD system with an untrusted noise model and neutral party model, respectively. These analyses indicate that the neutral party model should be reasonably regarded as a general noise model, which will passively and greatly raise the performance of the system. Further, we propose a dynamic auto-bias control scheme to actively resist the modulation noise which comes from the drift of bias point of the amplitude modulator. Together these methods contribute to the improvement of the practical performance of CVQKD systems with imperfect Gaussian modulation.

     

连续变量量子密钥分发系统中调制器驱动设计

相位调制器与振幅调制器是连续变量量子密钥分发中不可缺少的光调制器件.本文以量子安全通信系统的硬件为平台,设计了LiNbO3相位调制器的驱动电路,性能测试电路,同时给出了振幅调制器的性能监控电路.从理论与实验上对方案的可行性与可靠性进行了验证.     

Arbitrated Quantum Signature Scheme with Continuous-Variable Coherent States

Motivated by the revealing features of the continuous-variable (CV) quantum cryptography, we suggest an arbitrated quantum signature (AQS) protocol with CV coherent states. It involves three participants, i.e., the signer Alice, the verifier Bob and the arbitrator Charlie who is trustworthy by Alice and Bob. Three phases initializing phase, signing phase and verifying phase are included in our protocol. The security of the signature scheme is guaranteed by the generation of the shared keys via the CV-based quantum key distribution (CV-QKD) and the implementation process of the CV-based quantum teleportation as well. Security analysis demonstrates that the signature can be neither forged by anyone nor disavowed by the receiver and signer. Moreover, the authenticity and integrality of the transmitted messages can be ensured. The paper shows that a potential high-speed quantum signature scheme with high detection efficiency and repetition rate can be realized when compared to the discrete-variable (DV) quantum signature scheme attributing to the well characteristics of CV-QKD.     

Application of a Discrete Phase-Randomized Coherent State Source in Round-Robin Differential Phase-Shift Quantum Key Distribution

Recently, a novel kind of quantum key distribution called the round-robin differential phase-shift(RRDPS)protocol was proposed, which bounds the amount of leakage without monitoring signal disturbance. The protocol can be implemented by a weak coherent source. The security of this protocol with a simply characterized source has been proved. The application of a common phase shift can improve the secret key rate of the protocol. In practice, the randomized phase is discrete and the secret key rate is deviated from the continuous case. In this study, we analyze security of the RRDPS protocol with discrete-phase-randomized coherent state source and bound the secret key rate. We fix the length of each packet at 32 and 64, then simulate the secret key rates of the RRDPS protocol with discrete-phase randomization and continuous-phase randomization. Our simulation results show that the performance of the discrete-phase randomization case is close to the continuous counterpart with only a small number of discrete phases. The research is practically valuable for experimental implementation.     

Practical Analysis of Continuous-Variable Quantum Key Distribution Using a Nondeterministic Noiseless Linear Amplifier

We study the impact of the imperfections and the finite-size effect on the continuous-variable quantum key distribution (CVQKD) protocol with the nondeterministic noiseless linear amplifier (NLA). The imperfections of the homodyne detector and the imperfect amplification process as well as the finite-size effect on parameter estimation procedure are considered. We can see that despite the imperfections of the homodyne detector, the maximum improved transmission distance can still reach the equivalence of 20log₁₀g dB losses theoretically. Moreover, the analysis shows the imperfect amplification process of the NLA will slightly decrease the performance of the system. And we find the finite-size effect significantly influence the secret key rates of the NLA CVQKD protocol and the performance will approach the ideal asymptotic case with the increase of block size.     

Four-State Modulation in Middle of a Quantum Channel for Continuous-Variable Quantum Key Distribution Protocol with Noiseless Linear Amplifier

We characterize a modified continuous-variable quantum key distribution(CV-QKD)protocol with four states in the middle of a quantum channel.In this protocol,two noiseless linear amplifiers(NLAs) are inserted before each detector of the two parts,Alice and Bob,with the purpose of increasing the secret key rate and the maximum transmission distance.We present the performance anal.ysis of the new four-state CV-QKD protocol over a Gaussian lossy and noisy channel.The simulation results show that the NLAs with a reasonable gain g can effectively enhance the secret key rate as well as the maximum transmission distance,which is generally satisfied in practice.     

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water's optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable(CV) quantum key distribution(QKD) based air-to-water channel. The effects of the absorption and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously.Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.