Secret Key Rate Research Articles

Continuous-variable quantum key distribution with on-chip light sources

Integrated quantum key distribution (QKD) systems based on photonic chips have high scalability and stability, and are promising for further construction of global quantum communications networks. On-chip quantum light sources are a critical component of a fully integrated QKD system; especially a continuous-variable QKD (CV-QKD) system based on coherent detection, which has extremely high requirements for the light sources. Here, for what we believe is the first time, we designed and fabricated two on-chip tunable lasers for CV-QKD, and demonstrated a high-performance system based on these sources. Because of the high output power, fine tunability, and narrow linewidth, the involved on-chip lasers guarantee the accurate shot-noise-limited detection of quantum signals, center wavelength alignment of nonhomologous lasers, and suppression of untrusted excess noise. The system’s secret key rate can reach 0.75 Mb/s at a 50 km fiber distance, and the secure transmission distance can exceed 100 km. Our results mark a breakthrough toward building a fully integrated CV-QKD, and pave the way for a reliable and efficient terrestrial quantum-secure metropolitan area network.

Tapping Eavesdropper Designs Against Physical Layer Secret Key in Point-to-Point Fiber Communications

With the growing demand for service access and data transmission, security issues in optical fiber systems have become increasingly important and the subject of increased research. Physical layer secret key generation (PL-SKG), which leverages the random but common channel properties at legitimate parties, has been shown to be a secure, low-cost, and easily deployed technique as opposed to computational-based cryptography, quantum, and chaos key methods that rely on precise equipment. However, the eavesdropper (Eve) potential for current PL-SKG in fiber communications has been overlooked by most studies to date. Unlike wireless communications, where the randomness comes from the spatial multi-paths that cannot be all captured by Eves, in fiber communications, all the randomness (from transmitted random pilots or channel randomness) is contained in the signals transmitted inside the fiber. This, therefore, enables a tapping Eve to reconstruct the common features of legitimate users from its received signals, and further decrypt the featured-based secret keys. To implement this idea, we designed two Eve schemes against polarization mode distortion (PMD) based PL-SKG and the two-way cross multiplication based PL-SKG. The simulation results show that our proposed Eves can successfully reconstruct the legitimate common feature and the secret key relied upon, leading to secret key rate (SKR) reductions of between three and four orders of magnitude in the PL-SKG schemes studied. As a result, we reveal and demonstrate a novel eavesdropping potential to provide challenges for current physical layer secret key designs. We hope to provide more insightful vision and critical evaluation on the design of new physical layer secret key schemes in optical fiber links, to provide more comprehensively secure, and intelligent optical networks.

Efficient room-temperature molecular single-photon sources for quantum key distribution.

Quantum key distribution (QKD) allows the distribution of cryptographic keys between multiple users in an information-theoretic secure way, exploiting quantum physics. While current QKD systems are mainly based on attenuated laser pulses, deterministic single-photon sources could give concrete advantages in terms of secret key rate (SKR) and security owing to the negligible probability of multi-photon events. Here, we introduce and demonstrate a proof-of-concept QKD system exploiting a molecule-based single-photon source operating at room temperature and emitting at 785 nm. With an estimated maximum SKR of 0.5 Mbps, our solution paves the way for room-temperature single-photon sources for quantum communication protocols.

Evaluation of Quantum Key Distribution for Secure Satellite-integrated IoT Networks

There has been a dramatic increase in the number of Internet of Things (IoT) devices and their applications. Furthermore, there is a growing impetus to integrate IoT networks on a global scale, using satellites to expand the range of IoT connectivity into geographically remote areas. Ensuring the security of satellite backhaul for IoT networks is thus of paramount importance. The steady advance of quantum computing in recent years threatens to nullify classical cryptographic approaches based on assumptions of computational hardness, motivating the need for post-quantum cryptography. Quantum computing algorithms have been developed that, once a quantum computer of sufficient scale is realised, will be able to break classical cryptosystems efficiently (at polynomial-time complexity). A promising method of securing information against this threat at the physical layer has emerged in the form of quantum key distribution (QKD). QKD exploits the fundamental physical properties of light to guarantee information-theoretic security. Research into the application and standardisation of QKD to secure satellite backhaul, however, is still in its infancy. This paper presents a brief overview of the theoretical basis for QKD, whilst also providing a survey of contemporary QKD protocols. It evaluates the ability of these protocols to secure satellite backhaul in the context of a typical satellite-IoT network architecture. Furthermore, it highlights the vulnerabilities, as well as the technical challenges associated with this endeavour. Finally, it proposes directions for future research and development into protocols and standardisation for the satellite-integrated IoT domain. Several challenges must be overcome before QKD can evolve into a global-scale solution for securing satellite-IoT. Secret key generation rate remains very low in practical demonstrations of trusted-relay QKD satellite architectures. Further research is needed to overcome or mitigate the fundamental rate-distance trade-off before satellite QKD can be considered practicable in an IoT application. Alternatives that do not rely on trusted nodes are contingent on nascent technologies such as quantum repeaters and quantum memory. Whilst in theory QKD provides perfect information-theoretic security, it remains vulnerable to attacks that exploit imperfections in real-world equipment. Further effort is needed to develop QKD protocols that can safeguard against the aforementioned challenges.

Improving the performance of reference-frame-independent quantum key distribution with advantage distillation technology.

The reference-frame-independent quantum key distribution (RFI-QKD) has the advantage of tolerating reference frames that slowly vary. It can generate secure keys between two remote users with slowly drifted and unknown reference frames. However, the drift of reference frames may inevitably compromise the performance of QKD systems. In the paper, we employ the advantage distillation technology (ADT) to the RFI-QKD and the RFI measurement-device-independent QKD (RFI MDI-QKD), and we then analyze the effect of ADT on the performance of decoy-state RFI-QKD and RFI MDI-QKD in both asymptotic and nonasymptotic cases. The simulation results show that ADT can significantly improve the maximum transmission distance and the maximum tolerable background error rate. Furthermore, the performance of RFI-QKD and RFI MDI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are taken into account. Our work combines the merits of the ADT and RFI-QKD protocols, which further enhances the robustness and practicability of QKD systems.

Multipartite quantum cryptography based on the violation of Svetlichny’s inequality

Multipartite cryptography is useful for some particular missions. In this paper, we present a quantum key distribution scheme in which three separated observers can securely share a set of keys by using a sequence of 3-particle GHZ states. We prove that the violation of Svetlichny’s inequality can be utilized to test for eavesdropping, and even when the eavesdropper can completely control the outcomes of two participants’ measurements, our scheme still ensures the security of the keys distribution. This scheme can be easily extended to the case of N-party keys distribution, and the violation of N-partite Svetlichny’s inequality guarantees the security of the generalized scheme. Since the GHZ state has maximum entanglement, its perfect monogamy guarantee the device-independent security of our protocol. However, quantum entanglement is a vulnerable resource which is often decayed during transmission, so we need here to derive the secret-key rate of our protocol under the condition of using quantum states with non-maximal entanglement. We then calculate the extractable secret-key rate of the three-party key distribution protocol for the Werner state in the device-independent scenario. We find that the value of the extractable secret-key rate monotonously approaches 1 as the value of the visibility of the Werner state increases, and it reaches its maximum value 1 when the Werner state becomes the GHZ state.

Performance analysis for OFDM-based multi-carrier continuous-variable quantum key distribution with an arbitrary modulation protocol.

Multi-carrier continuous-variable quantum key distribution (CV-QKD) is considered to be a promising way to boost the secret key rate (SKR) over the existing single-carrier CV-QKD scheme. However, the extra excess noise induced in the imperfect multi-carrier quantum state preparation process of N subcarriers will limit the performance of the system. Here, a systematic modulation noise model is proposed for the multi-carrier CV-QKD based on the orthogonal frequency division multiplexing (OFDM). Subsequently, the performance of multi-carrier CV-QKD with arbitrary modulation protocol (e.g. QPSK, 256QAM and Gaussian modulation protocol) can be quantitatively evaluated by combining the security analysis method of the single-carrier CV-QKD. Under practical system parameters, the simulation results show that the SKR of the multi-carrier CV-QKD can still be significantly improved by increasing the carrier number N even with imperfect practical modulations. Specifically, the total SKR of multi-carrier CV-QKD can be optimized by carefully choosing N. The proposed model provides a feasible theoretical framework for the future multi-carrier CV-QKD experimental implementation.

Small-form-factor Gaussian-modulated coherent-state transmitter for CV-QKD using a gain-switched DFB laser.

We report a directly modulated distributed feedback laser operating in gain-switching mode for preparing the coherent states required for the Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) protocol. The proposed single-component quantum transmitter design eliminates the need for external modulators, decreasing the complexity of GMCS CV-QKD systems. The experimental results demonstrate a potential asymptotic secret key rate value of 2.63 Mbps over an 11-km fiber link, making the directly modulated GMCS transmitter particularly suitable for metropolitan optical networks where compactness, robustness, and low cost are key desirable features.

Satellite continuous-variable quantum key distribution systems using code-division multiple access

In this paper, we propose a novel architecture of the satellite continuous-variable quantum key distribution (CV-QKD) system that can not only support multiple users but also enhance the security. The satellite CV-QKD system is based on a code-division multiple access (CDMA) technique to simultaneously transmit multiple key streams from a trusted satellite to a ground station, which passively forwards these key streams to multiple users nearby via optical fibers. Our proposed architecture avoids using multiple ground stations that result in high costs. We analyze the performance of the proposed system under the negative impacts of atmospheric attenuation and atmospheric turbulence, as well as beam spreading and pointing error loss. Especially, the impact of multiple user interference is also considered in our analysis. The numerical results show that the proposed QKD system using CDMA can support multiple users, whose performance metrics such as quantum bit-error rate (QBER), sifted probability, and secret key rate meet the designed targets. The eavesdroppers suffer high QBER and low sifted probability, thus the security is guaranteed.

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using 10^{16} signals. Moreover, the expected secret key rate was simulated to examine our protocol’s performance at various intrinsic error rate values, Q=(0.3%,0.6%,1%) caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about 10^{14} signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

Eavesdropping a quantum key distribution network using sequential quantum unsharp measurement attacks

We investigate the possibility of eavesdropping on a quantum key distribution network by local sequential quantum unsharp measurement attacks by the eavesdropper. In particular, we consider a pure two-qubit state shared between two parties Alice and Bob, sharing quantum steerable correlations that form the one-sided device-independent quantum key distribution network. One qubit of the shared state is with Alice and the other one while going to Bob’s place is intercepted by multiple sequential eavesdroppers who perform quantum unsharp measurement attacks thus gaining some positive key rate while preserving the quantum steerable correlations for Bob. In this way, Bob will also have a positive secret key rate although reduced. However, this reduction is not that sharp and can be perceived due to the decoherence and imperfection of the measurement devices. We found that there is a possibility of sequential eavesdropping even after setting a minimum threshold on the observed secure key rate by Alice and Bob. In the end, we show that an unbounded number of eavesdroppers can also get secret information in some specific scenario.

Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement

In this work, we introduce multipartite intrinsic non-locality as a method for quantifying resources in the multipartite scenario of device-independent (DI) conference key agreement. We prove that multipartite intrinsic non-locality is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for two variants of multipartite mutual information, which we then use to prove that multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.

Implementation of encoder and decoder for low-density parity-check codes in continuous-variable quantum key distribution on a field programmable gate array

Quantum key distribution (QKD) can provide an unconditionally secure communication encryption method. Continuous-variable QKD (CVQKD) requires extracting the key from the noisy channel, leading to higher requirements for the error-correcting codes used in multidimensional reconciliation. We extend the quasi-cyclic low-density parity-check of the radio design for the global 5G mobile communication technology standard to achieve error correction under lower signal-to-noise ratio on integrated hardware. A field programmable gate array (FPGA) chip is used to realize the approximate lower triangular matrix encoding algorithm, and the core module only has the circular shift register, which reduces the encoding complexity, improves the encoding efficiency, and reduces the hardware resource consumption. For extended super-long code words, the decoding algorithm requires additional hardware resources to implement, which the previous algorithm cannot meet. Therefore, we present a hardware implementation of offset minimum sum algorithm (OMSA), which can avoid operations of complex mathematical formula. The offset factor of OMSA reduce the error caused by the low accuracy of calculation on the hardware. The update of the decoding information is layered in a partially parallel way in the matrix to achieve the cross processing of node information. It speeds up the transmission of information between different nodes and the convergence of decoding algorithm of low-complexity parallel structure. Simulation results show that the maximum theoretical coordination efficiency is 85% when the code with block length is 69632 at a bit rate of 22/68 and the signal-to-noise ratio asymptotic threshold is 0.7. Using an FPGA, ∼0.1 frame error rate was achieved, but with a zero-bit error rate, the optimal achievable secret key rate is about 200 Kbps at 30-km distance theoretically. For a 200-MHz system clock on the successfully decoded block, 125 Gbps encoding throughput and 472 Kbps decoding throughput was achieved, better than the theoretical key rate of prototype of CVQKD.

Reference-frame-independent quantum key distribution with advantage distillation.

Advantage distillation (AD) provides a means of separating highly correlated raw key bits from weakly correlated information in quantum key distribution (QKD). In this Letter, we apply the AD method to improve the performance of reference-frame-independent QKD (RFI-QKD). Simulation results show that, compared with RFI-QKD without AD, RFI-QKD with AD can tolerate higher system errors and obtain better performance on the secret key rate and transmission distance. Furthermore, we extend the AD method to RFI measurement-device-independent QKD (RFI-MDI-QKD) and demonstrate that the AD method can improve the performance of RFI-MDI-QKD more significantly.

Security against Collective Attacks for a Continuous-Variable Quantum Key Distribution Protocol Using Homodyne Detection and Postselection

We analyze the security against collective attacks for a homodyne-based continuous-variable quantum key distribution protocol using binary coherent states and postselection. We derive a lower bound of the secret key rate in an asymptotic scenario, and numerically optimize it for the case of a symmetric Gaussian channel.

Ultrafast quantum key distribution using fully parallelized quantum channels.

The field of quantum information processing offers secure communication protected by the laws of quantum mechanics and is on the verge of finding wider application for the information transfer of sensitive data. To improve cost-efficiency, extensive research is being carried out on the various components required for high data throughput using quantum key distribution (QKD). Aiming for an application-oriented solution, we report the realization of a multichannel QKD system for plug-and-play high-bandwidth secure communication at telecom wavelengths. We designed a rack-sized multichannel superconducting nanowire single photon detector (SNSPD) system, as well as a highly parallelized time-correlated single photon counting (TCSPC) unit. Our system is linked to an FPGA-controlled QKD evaluation setup for continuous operation, allowing us to achieve high secret key rates using a coherent-one-way protocol.

Countermeasure for Negative Impact of a Practical Source in Continuous-Variable Measurement-Device-Independent Quantum Key Distribution

Continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) can fundamentally defend all attacks on the measurement devices. Consequently, higher requirements are put forward for the source of a CV-MDI QKD system. However, the imperfections of the actual source brings practical security risks to the CV-MDI QKD system. Therefore, the characteristics of the realistic source must be controlled in real time to guarantee the practical security of the CV-MDI QKD system. Here we propose a countermeasure for negative impact introduced by the actual source in the CV-MDI QKD system based on the one-time-calibration method, not only eliminating the loophole induced from the relative intensity noise (RIN), which is part of the source noise, but also modeling the source noise thus improves the performance. In particular, three cases in terms of whether the preparation noise of the practical sources are defined or not, where only one of the users or both of the two users operate monitoring on their respective source outputs, are investigated. The simulation results show that the estimated secret key rate without our proposed scheme is about 10.7 times higher than the realistic rate at 18 km transmission distance when the variance of RIN is only 0.4. What is worse, the difference becomes greater and greater with the increase of the variance of RIN. Thus, our proposed scheme makes sense in further completing the practical security of the CV-MDI QKD system. In other words, our work enables the CV-MDI QKD system not only to resist all attacks against detectors, but also to close the vulnerability caused by the actual source, thus making the scheme closer to practical security.

MIMO Terahertz Quantum Key Distribution Under Restricted Eavesdropping

Quantum key distribution (QKD) can provide unconditional security to next generation communication networks guaranteed by the laws of quantum physics. This paper studies the secret key rate (SKR) of a continuous variable quantum key distribution (CV-QKD) system using multiple-input multipleoutput (MIMO) transmission and operating at Terahertz (THz) frequencies. Distinct from previous works, we consider a practical “restricted" eavesdropping scenario in which Eve can collect only a fraction of photons lost in the environment. We propose a system model for the MIMO THz CV-QKD system that accounts for restricted eavesdropping via a lossy wireless channel between Alice and Eve. We derive for this system new SKR expressions for both coherent-state-based and squeezed-state-based CV-QKD protocols. Our results show that previous analysis assuming unrestricted eavesdropping leads to overly pessimistic SKRs, and that in practice, the achievable SKR can be significantly increased under restricted eavesdropping. The increase in the SKR is quantified by the simplified SKR expansions derived in this paper. Our results also reveal that squeezing is beneficial for improving the SKR only for unrestricted eavesdropping. However, in a practical setting with restricted eavesdropping, increased squeezing leads to a reduction in the SKR.

Millimeter-Waves to Terahertz SISO and MIMO Continuous Variable Quantum Key Distribution

With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannon's channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> = 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> =100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5km at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> =100GHz and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> =4K by using 1024×1024 antennas. Our results for the first time show the possibility of mm-waves and THz MIMO CVQKD with the system operating at temperatures below <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> = 50K, which may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space to indoor and short-distance communications.

Security Analysis of Triangle Channel-Based Physical Layer Key Generation in Wireless Backscatter Communications

Ambient backscatter communication (AmBC) enables ultra-low-power communications by backscattering ambient radio frequency (RF) signals and harvesting energy simultaneously. It has emerged as a cutting-edge technology for supporting a variety of Internet of Things (IoT) applications. However, existing research lacks effective secret key sharing schemes for safeguarding communications between resource-constrained backscatter devices (BDs) in AmBC systems. In this paper, we present, Tri-Channel, a novel physical layer key generation scheme between two BDs by multiplying downlink signals and backscatter signals to obtain the information of a triangle channel as a shared random secret source for key generation. In particular, we analyze the security of our scheme under both passive and active attacks, concretely Eavesdropping Attack (EA), Control Channel Attack (CCA), Signal Manipulative Attack (SMA), and Untrusted RF-Source Attack (URSA). Through theoretical analysis and simulations by comparing with a traditional scheme (named Tradi-Channel), we found that our scheme consistently outperforms the Tradi-Channel under the EA and two active attacks (CCA and SMA). In addition, it shows better security performance under URSA, which is proposed based on the unauthenticated characteristic of BDs in Tri-Channel, even though URSA is more vital than SMA. Concretely, Tri-Channel’s secret key rate (SKR) outperforms Tradi-Channel’s under the above four passive and active attacks. This implies that our scheme is advanced in terms of both security and efficiency of key generation. Numerous extensive simulations further prove our theoretical analysis results.