Achievable Secret Key Rate Research Articles

Mapping Guaranteed Positive Secret Key Rates for Continuous Variable Quantum Key Distribution.

The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol's capability to produce positive SKRs.

Simulation of an entanglement-based quantum key distribution protocol

Since the 80 s when it was first proposed, Quantum Key Distribution (QKD) elicited great interest in the field of cryptography as a unique procedure for key generation that could in principle guarantee unconditionally secure communication “by the laws of Physics”. In the last fifteen years commercial solutions have started appearing on the market, showing that practical implementations of the protocol were not only possible but also competitive in terms of security and achievable secret-key rate. In this work we describe a simulation of the historical QKD protocol E91 on the IBM Quantum platform, making use of the qubit formalism to represent the quantum states received by two communicating nodes. Having implemented also the post-processing steps for the error correction and the privacy amplification, this model can represent a simple stand-alone tool to study the performance not only of one-to-one communication but of more complex systems that rely on QKD for security, one above all QKD networks.

A Best-Path Approach to the Design of a Hybrid Space–Ground Quantum Network with Dynamic Constraints

The design and operation of quantum networks are both decisive in the current push towards a global quantum internet. Although space-enabled quantum connectivity has already been identified as a beneficial candidate for long-range quantum channels for over two decades, the architecture of a hybrid space–ground network is still a work in progress. Here, we propose an analysis of such a network based on a best-path approach, where either fiber- or satellite-based elementary links can be concatenated to form a repeater chain. The network consisting of quantum information processing nodes, equipped with both ground and space connections, is mapped into a graph structure, where edge weights represent the achievable secret key rates, chosen as the figure of merit for the network analysis. A weight minimization algorithm allows for identifying the best path dynamically, i.e., as the weather conditions, stray light radiance, and satellite orbital position change. From the results, we conclude that satellite links will play a significant role in the future large-scale quantum internet, in particular when node distances exceed 500 km, and both a constellation of satellites—spanning 20 or more satellites—and significant advances in filtering technology are required to achieve continuous coverage.

Practical, high-speed Gaussian coherent state continuous variable quantum key distribution with real-time parameter monitoring, optimised slicing, and post-processed key distillation

Gaussian coherent state continuous variable quantum key distribution has gained interest owing to its security and compatibility with classical coherent optical fibre networks. For successful system deployment it is necessary to implement practical high speed systems which distil keys efficiently. Here, we demonstrate a Gaussian coherent state continuous variable quantum key distribution system at a 50 MHz symbol rate. Unlike most demonstrations to date which measure excess noise and infer key rates from this, we record signals in real time and distil keys. We also demonstrate, for the first time, slice reconciliation with optimised guard bands to maximise achievable secret key rates. Using this optimisation with multilevel slicing, a record 5 Mb/s secret key rate after a transmission distance of 25 km is achieved. This is a significant improvement on the 3 Mb/s secret key rate which is achieved with single level optimised slice reconciliation.

Secret key rate bounds for quantum key distribution with faulty active phase randomization

Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization in an active setup, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD when the phase is actively randomized by faulty devices, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.

Arbitrary bias control of LiNbO3 based Mach-Zehnder intensity modulators for QKD system

Quantum key distribution (QKD) can help distant agents to share unconditional secret keys, and the achievable secret key rate can be enhanced with the help of decoy-state protocol. To implement QKD experimentally, the agents are supposed to accurately transmit a number of different intensity pulses with the LiNbO3 based Mach-Zehnder (LNMZ) intensity modulator. However, the bias drift of LNMZ intensity modulator may affect the performance of a QKD system. In this letter, we reveal a simple RC circuit model to demonstrate the bias drift in the LNMZ intensity modulator. And based on the model, we propose a multi-step bias stable scheme to control the bias working point. Experimental result shows that our scheme can eliminate the bias drift of at arbitrary working point within a long time range. Besides, there is no need of any feedback mechanisms in the scheme. This means our scheme will not lead to any increasement in system complexity, making it more suitable for a QKD system.

Information Rates With Non Ideal Photon Detectors in Time-Entanglement Based QKD

We develop new methods of quantifying the impact of photon detector imperfections on possible secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and dark photon counts and show how each may decrease the maximum achievable secret key rate differently. We begin with a standard Discrete Memoryless Channel (DMC) model to get a good bound on the mutual information lost due to the timing jitter, then introduce a novel Markov Chain (MC) based model to characterize the effect of detector downtime and show how it introduces memory to the key generation process. Finally, we propose a new method of including dark counts in the analysis that shows how dark counts can be especially detrimental when using the common Pulse Position Modulation (PPM) for key generation. Our results show that these three imperfections can significantly reduce the achievable secret key rate when using PPM for QKD. One of our main results is providing tooling for experimentalists to predict their systems’ achievable secret key rate given the detector specifications.

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.

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.

Time-division technique for quantum optical receivers utilizing single-photon detector array technology and spatial-multiplexing.

Free-space quantum key distribution (QKD) has been gaining popularity in recent years due to its advantages in creating networking options for the quantum internet. One of the main challenges to be addressed in QKD is the achievable secret key rate, which must meet current and future demand. Some of the existing solutions include the use of higher bandwidth electronics, untrusted relay architectures such as Twin-Field QKD, or high dimensional QKD. In this work, we proposed the use of a combination of spatial-multiplexing and time-division techniques, together with the use of 2D single-photon avalanche diode arrays to increase the final throughput. The main challenge in a free-space scenario is the effects introduced by turbulence. This paper demonstrates how appropriate time-division of the spatial-modes can reduce the quantum bit error rate due to optical crosstalk from 36% to 0%. With this technique, we believe the future need for superconducting nanowires single photon detectors, in some free-space QKD applications, can be relaxed, obtaining more cost-effective receiver systems.

Hardware-Impaired PHY Secret Key Generation With Man-in-the-Middle Adversaries

In this letter, we examine the PHY layer secret key generation (PHY-SKG) scheme in the presence of man-in-the-middle (MiM) adversary, while legitimate parties suffer from <i>hardware impairments</i> (HIs). Different from previous works on PHY-SKG that consider adversaries who simply try to make an interference in the communication link, the MiM aims to deceive legitimate entities about the source of common randomness. To conquer the MiM attack, legitimate parties utilize randomized pilots (RPs) in our proposed scheme. We analyze the effect of HIs on the performance of system by deriving the achievable secret key rate (SKR). Our results highlight a fundamental limit, as a ceiling phenomena, on the SKR when having practical imperfections. Top-level guidelines for selecting impairment levels along the transceiver chains is also provided to maximize the performance of the PHY-SKG protocol. Our numerical results verify the analytic expressions derived, while providing insights on system design. We show that by properly considering the HIs, about 25&#x0025; improvement in the SKR is achievable.

Computing secure key rates for quantum cryptography with untrusted devices

Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input–output statistics of the devices to achieve information-theoretic security. Although the basic security principles of DIQKD are now well understood, it remains a technical challenge to derive reliable and robust security bounds for advanced DIQKD protocols that go beyond the previous results based on violations of the CHSH inequality. In this work, we present a framework based on semidefinite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input–output probability distribution or any choice of Bell inequality. Our method also extends to other DI cryptographic tasks.

Securing the Inter-Spacecraft Links: Physical Layer Key Generation From Doppler Frequency Shift

In this work, we propose a secret key generation procedure specifically designed for the inter-spacecraft communication links. As a novel secrecy source, the spacecrafts utilize Doppler frequency shift based measurements. In this way, the mobilities of the communication devices are exploited to generate secret keys, where this resource can be utilized in the environments that the channel fading based key generation methods are not available. The mobility of a spacecraft is modeled as the superposition of a pre-determined component and a dynamic component. We derive the maximum achievable secret key generation rate from the Doppler frequency shift. The proposed secret key generation procedure extracts the Doppler frequency shift in the form of nominal power spectral density samples (NPSDS). We propose a maximum-likelihood (ML) estimation for the NPSDS at the spacecrafts, then a uniform quantizer is utilized to obtain secret key bits. The key disagreement rate (KDR) is analytically obtained for the proposed key generation procedure. Through numerical studies, the tightness of the provided approximations is shown. Both the theoretical and numerical results demonstrate the validity and the practicality of the presented physical layer key generation procedure considering the security of the communication links of spacecrafts.

Reference frame independent twin field quantum key distribution with source flaws

The trade-off between distance and secret key generation rate remains one of the major challenges in the practical implementation of quantum key distribution (QKD). As a solution, a twin field QKD protocol was proposed by Lucamarini et al (2018) to address this challenge. In this protocol, the achievable secret key rate scales with the square root of channel transmittance and can surpass the secret key capacity for repeaterless QKD. However, the protocol exploits phase to encode information which presents the problem of active stabilization of interferometers. We propose a reference frame independent twin field quantum key distribution (RFITF QKD), which does not require the reference frames’ alignment. Thus, this reduces the complexity of practical QKD systems in achieving active stabilization of phase. Moreover, we employ the loss-tolerant method proposed by Tamaki et al (2014) which allows us to prove the security of the protocol by considering imperfections in the state preparation. Our simulation results show that our proposed protocol can extract a secure key over a transmission distance of l = 505 km, l = 516 km and l = 530 km for deviation of 8.42°, 7.28° and 5.15°, respectively from the desired phase encoding angle. These results demonstrate that despite the state preparation flaws, the key rates achieved are still comparable to the perfect encoding scenario. When our proposed protocol is implemented with an imperfect source, it achieves a transmission distance beyond the secret key capacity bound for repeaterless QKD.

Enhancing discrete-modulated continuous-variable measurement-device-independent quantum key distribution via quantum catalysis

Discrete modulation can make up for the shortage of transmission distance in measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD), providing a unique advantage against all side-channel attacks but also creating a challenge for further performance improvement. Here we suggest a quantum catalysis (QC) approach for enhancing the performance of the discrete-modulated (DM) MDI-CVQKD in terms of the achievable secret key rate and lengthening the maximal transmission distance. The numerical simulation results show that the QC-based MDI-CVQKD with discrete modulation, involving a zero-photon catalysis (ZPC) operation, can not only obtain a higher secret key rate than the original DM protocol, but also contribute to a reasonable increase of the corresponding optimal variance. As for the extreme asymmetric and symmetric cases, the secret key rate and maximal transmission distance of the ZPC-involved DM MDI-CVQKD system can be further improved under the same parameters. This approach enables the system to tolerate lower reconciliation efficiency, which may provide excellent potential for practical implementations with state-of-art technology.

Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits

Quantum communication technologies show great promise for applications ranging from the secure transmission of secret messages to distributed quantum computing. Due to fiber losses, long-distance quantum communication requires the use of quantum repeaters, for which there exist quantum memory-based schemes and all-photonic schemes. While all-photonic approaches based on graph states generated from linear optics avoid coherence time issues associated with memories, they outperform repeater-less protocols only at the expense of a prohibitively large overhead in resources. Here, we consider using matter qubits to produce the photonic graph states and analyze in detail the trade-off between resources and performance, as characterized by the achievable secret key rate per matter qubit. We show that fast two-qubit entangling gates between matter qubits and high photon collection and detection efficiencies are the main ingredients needed for the all-photonic protocol to outperform both repeater-less and memory-based schemes.

Composable finite-size effects in free-space continuous-variable quantum-key-distribution systems

Free-space channels provide the possibility of establishing continuous-variable quantum key distribution in global communication networks. However, the fluctuating nature of transmissivity in these channels introduces an extra noise which reduces the achievable secret key rate. We consider two classical postprocessing strategies, postselection of high-transmissivity data and data clusterization, to reduce the fluctuation-induced noise of the channel. We undertake the investigation of such strategies utilizing a composable security proof in a realistic finite-size regime against both collective and individual attacks. We also present an efficient parameter estimation approach to estimate the effective Gaussian parameters over the postselected data or the clustered data. Although the composable finite-size effects become more significant with the postselection and clusterization both reducing the size of the data, our results show that these strategies are still able to enhance the finite-size key rate against both individual and collective attacks with a remarkable improvement against collective attacks, even moving the protocol from an insecure regime to a secure regime under certain conditions.

Asymptotic security of discrete-modulation protocols for continuous-variable quantum key distribution

We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.

A Lightweight Secure and Resilient Transmission Scheme for the Internet of Things in the Presence of a Hostile Jammer

In this article, we propose a lightweight security scheme for ensuring both information confidentiality and transmission resiliency in the Internet-of-Things (IoT) communication. A single-antenna transmitter communicates with a half-duplex single-antenna receiver in the presence of a sophisticated multiple-antenna-aided passive eavesdropper and a multiple-antenna-assisted hostile jammer (HJ). A low-complexity artificial noise (AN) injection scheme is proposed for drowning out the eavesdropper. Furthermore, for enhancing the resilience against HJ attacks, the legitimate nodes exploit their own local observations of the wireless channel as the source of randomness to agree on shared secret keys. The secret key is utilized for the frequency hopping (FH) sequence of the proposed communication system. We then proceed to derive a new closed-form expression for the achievable secret key rate (SKR) and the ergodic secrecy rate (ESR) for characterizing the secrecy benefits of our proposed scheme, in terms of both information secrecy and transmission resiliency. Moreover, the optimal power sharing between the AN and the message signal is investigated with the objective of enhancing the secrecy rate. Finally, through extensive simulations, we demonstrate that our proposed system model outperforms the state-of-the-art transmission schemes in terms of secrecy and resiliency. Several numerical examples and discussions are also provided to offer further engineering insights.

Continuous-variable measurement-device-independent quantum key distribution via quantum catalysis

The continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) is a promising candidate for the immunity to side-channel attacks, but unfortunately seems to face the limitation of transmission distance in contrast to discrete-variable (DV) counterpart. In this paper, we suggest a method of improving the performance of CV-MDI-QKD involving the achievable secret key rate and transmission distance by using zero-photon catalysis (ZPC), which is indeed a noiseless attenuation process. The numerical simulation results show that the transmission distance of ZPC-based CV-MDI-QKD under the extreme asymmetric case is better than that of the original protocol. Attractively, in contrast to the previous single-photon subtraction (SPS)-based CV-MDI-QKD, the proposed scheme enables a higher secret key rate and a longer transmission distance. In particular, the ZPC-based CV-MDI-QKD can tolerate more imperfections of detectors than both the original protocol and the SPS-based CV-MDI-QKD.