CV-QKD Protocols Research Articles

Optimized-Eight-State CV-QKD Protocol Outperforming Gaussian Modulation Based Protocols

In this paper, an optimized-eight-state CV-QKD protocol is proposed significantly outperforming previously introduced discrete modulation (DM) protocols as well as the corresponding Gaussian modulation (GM)-based CV-QKD protocols for practical reconciliation efficiencies values in terms of both secret-key rate (SKR) and achievable distance. The proposed CV-QKD protocol also outperforms, in terms of SKR, the corresponding high-cost single-photon DV-QKD scheme, employing an array of multiplexed single-photon detectors, for several orders of magnitude. We also describe a generalized RF-assisted CV-QKD scheme with heterodyne detection applicable to arbitrary DM scheme, insensitive to the laser phase noise and frequency offset fluctuations.

Enhancing continuous variable quantum key distribution with a heralded hybrid linear amplifier

We propose a method to improve transmission distance of continuous-variable quantum key distribution via a heralded hybrid linear amplifier (HLA), involving an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The phase-insensitive amplification of quantum light states may experience a degradation of signal-to-noise ratio (SNR) of 3dB which can be surmounted by the probabilistic amplification process. The new hybrid amplifier allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. Our equipment could clone unknown coherent states with fidelity surpassing the no-cloning limit by abandoning determinism and using probabilistic methods. The setup has a better compatibility with continuous variable protocols as it only uses Gaussian elements and a post-selection algorithm. The hybrid linear amplifier enhances the SNR and hence the transmission distance of the CVQKD protocol is extended. Both the asymptotic secret key rate and the secret key rate in a finite-size scenario are analyzed in this paper.

Security Analysis of Practical Continuous-Variable Quantum Key Distribution Using a Heralded Noiseless Amplifier

The noiseless linear amplifier(NLA) can probabilistically amplify the amplitude of the coherent state while retaining the initial level of noise. It is widely proposed and discussed to enhance various CVQKD protocols. In the previous work, when analyzing the security of the NLA-based CVQKQ protocol, they usually included the impact of NLA in a set of equivalent parameters. In this article, we develop this equivalent method and propose a new one to analyze the protocol with NLA which simplifies the computational complexity. In particular, we have further considered the effect of NLA on entanglement parameter of the EPR state. Then by using our proposed method, we first obtain the secret key rate of the NLA-enhanced CVQKD system with imperfect detection. The results show that the NLA can also improve the transmission distance of CVQKD protocols with imperfect detection by equivalent $20\log _{10}g$ dB of losses.

Secret key rate proof of multicarrier continuous‐variable quantum key distribution

SummaryWe prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution CVQKD. In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier continuous variables (CVs). The multicarrier communication formulates Gaussian subchannels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single‐carrier Gaussian CVs. We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD. We derive the private classical capacity of a Gaussian subchannel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one‐way and two‐way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.

On the Photon Subtraction-Based Measurement-Device-Independent CV-QKD Protocols

To potentially overcome the practical security loopholes of CV-QKD protocols, in this paper, we propose to use the optimized eight-state measurement-device-independent (MDI) protocol and demonstrate that it can significantly outperform corresponding Gaussian modulation-based MDI and virtual photon subtraction-based MDI CV-QKD protocols in terms of both secret-key rate and achievable transmission distance. Contrary to the common belief that virtual photon subtraction method can extend the distance of MDI CV-QKD protocols, we show that this is not true for fully optimized MDI CV-QKD protocols and realistic system parameters.

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.

Efficient rate-adaptive reconciliation for CV-QKD protocol

Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CVQKD) systems. We propose an efficient rate-adaptive reconciliation protocol suitable for practical CV-QKD systems with time-varying quantum channel. This protocol changes the code rate of multi-edge type low density parity check codes, by puncturing (increasing the code rate) and shortening (decreasing the code rate) techniques, to enlarge the correctable signal-to-noise ratios regime, thus improves the overall reconciliation efficiency comparing to the original fixed rate reconciliation protocol. We verify our rate-adaptive reconciliation protocol with three typical code rate, i.e., 0.1, 0.05 and 0.02, the reconciliation efficiency keep around 93.5%, 95.4% and 96.4% for different signal-to-noise ratios, which shows the potential of implementing high-performance CV-QKD systems using single code rate matrix.

Teleportation-based continuous variable quantum cryptography

We present a continuous variable (CV) quantum key distribution (QKD) scheme based on the CV quantum teleportation of coherent states that yields a raw secret key made up of discrete variables for both Alice and Bob. This protocol preserves the efficient detection schemes of current CV technology (no single-photon detection techniques) and, at the same time, has efficient error correction and privacy amplification schemes due to the binary modulation of the key. We show that for a certain type of incoherent attack it is secure for almost any value of the transmittance of the optical line used by Alice to share entangled two-mode squeezed states with Bob (no 3 dB or 50% loss limitation characteristic of beam splitting attacks). The present CVQKD protocol works deterministically (no postselection needed) with efficient direct reconciliation techniques (no reverse reconciliation) in order to generate a secure key and beyond the 50% loss case at the incoherent attack level.

Non-Gaussian postselection and virtual photon subtraction in continuous-variable quantum key distribution

Photon subtraction can enhance the performance of continuous-variable quantum key distribution (CV QKD). However, the enhancement effect will be reduced by the imperfections of practical devices, especially the limited efficiency of a single-photon detector. In this paper, we propose a non-Gaussian postselection method to emulate the photon substraction used in coherent-state CV QKD protocols. The virtual photon subtraction not only can avoid the complexity and imperfections of a practical photon-subtraction operation, which extends the secure transmission distance as the ideal case does, but also can be adjusted flexibly according to the channel parameters to optimize the performance. Furthermore, our preliminary tests on the information reconciliation suggest that in the low signal-to-noise ratio regime, the performance of reconciliating the postselected non-Gaussian data is better than that of the Gaussian data, which implies the feasibility of implementing this method practically.

Controlling Continuous-Variable Quantum Key Distribution with Tuned Linear Optics Cloning Machines

We show that the tolerable excess noise can be elegantly controlled while inserting a tunable linear optics cloning machine (LOCM) for continuous-variable key distribution (CVQKD). The LOCM-tuned noise can be stabilized to an optimal value by the reference partner of reconciliation to guarantee the high secret key rate. Simulation results show that there is a considerable improvement of the performance for the LOCM-based CVQKD protocol in terms of the secret rate while making a fine balance between the secret key rate and the transmission distance with the dynamically tuned parameters in suitable ranges.

Geometrical analysis of physically allowed quantum cloning transformations for quantum cryptography

The security of quantum key distribution (QKD) relies on the no-cloning theorem, which allows no to copy perfectly a quantum system. An eavesdropping activity on the quantum channel perturbs the state of the quantum states, which results in noise at the receiver. The physical layer detection of the eavesdropping activity of the quantum channel requires tomography, which is intractable in experiment. An adequate and equivalent answer for the problem can be proposed through the logical layer. We propose an efficient algorithmical tool to study the eavesdropping activity on the quantum channel and characterize the properties of a quantum cloning-based attack for DV and CVQKD protocols. The physically allowed quantum cloning transformations on a quantum system can be described in terms of information geometry. We propose a computational geometrical method to analyze the cloning activity on the quantum channel and to characterize the noise properties. The security analysis studies the DV (discrete variable) and CV (continuous variable) QKD schemes through the four-state (BB84) and six-state DVQKD protocols and the two-way CVQKD protocol. The proposed geometrical method provides a useful tool to analyze the most powerful attacks against quantum cryptography and the effects of the physically allowed quantum cloning transformations.

Improving the maximum transmission distance of four-state continuous-variable quantum key distribution by using a noiseless linear amplifier

A modified four-state CVQKD protocol is proposed to increase the maximum transmission distance and tolerable excess noise in the presence of Gaussian lossy and noisy channel by using a noiseless linear amplifier (NLA). A NLA with amplitude gain g can increase the maximum admission losses by 20log(g) dB.

Bound on Noise of Coherent Source for Secure Continuous-Variable Quantum Key Distribution

Coherent source of continuous-variable quantum key distribution (CV QKD) system may become noisy in practical applications. The security of CV-QKD scheme with the noisy coherent source is investigated under realistic conditions of quantum channel and detector. In particular, two models are proposed to characterize the noisy coherent source through introducing a party (Fred) who induces the noise with an optical amplifier. When supposing the party Fred is untrusted, two lower security bounds to the noise of the coherent source are derived for reverse reconciliation and realistic homodyne and heterodyne detections. While supposing Fred is a neutral party, we derive two tight security bounds without knowing Fred’s exact state for ideal detections. Moreover, the simulation results show that the security of the reverse reconciliation CV-QKD protocols is very sensitive to the noise of coherent source for both the homodyne and heterodyne detections.

Improving the maximum transmission distance of coutinuous variable no-switching QKD protocol

Developing quantum key distribution (QKD) protocols that can resist losses and noises is of great importance in practice. We show that the maximum transmission distance and tolerable excess noise of the no-switching CV-QKD protocol can be dramatically increased by using a noiseless linear amplifier (NLA). It is proved that an NLA with a gain g can increase the maximum transmission distance by 20 log10g/α km, where α=0.2 dB/km is the loss coefficient of the fiber channel.

Tight bounds for the eavesdropping collective attacks on general CV-QKD protocols that involve non-maximally entanglement

A new method to quantify the eavesdropper's accessible information on continuous variable quantum key distribution for protocols implementing homodyne and heterodyne detections is introduced. We have derived upper bounds for the eavesdropping collective attacks on general continuous variable quantum key distribution protocols. Our focus is especially on deriving bounds which are Gaussian optimal for Eve collective attacks that involve non maximally entanglement (i.e. Alice and Bob use non maximally entangled states or non-Gaussian modulation for their quantum key distribution protocols). The new bounds derived are tight for all continuous variable quantum key distribution protocols. We show that the eavesdropper's accessible information is independent of the initial correlation between Alice and Bob modes in reverse reconciliation scheme, while in direct reconciliation scheme, Eve information is given as a function of Alice and Bob initial correlation.