Quantum Key Distribution Scheme Research Articles

High-dimensional temporal mode propagation in a turbulent environment

Temporal modes of photonic quantum states, intrinsically possess high dimensional Hilbert spaces, provide a new framework to develop a robust free-space quantum key distribution (QKD) scheme in a maritime environment. We show that the high-dimensional temporal modes can be used to fulfill a persistent communication channel to achieve high photon-efficiency even in severe weather conditions. We identify the parameter regimes that allow for a high-fidelity quantum information transmission. We also examine how the turbulent environment affects fidelity and entanglement degree in various environmental settings.

An Intrusion Resistant SCADA Framework Based on Quantum and Post-Quantum Scheme

The rapid emergence of quantum computing threatens current Supervisory Control and Data Acquisition (SCADA) security standards, mainly, American Gas Association (AGA)-12. Therefore, researchers are developing various security schemes based on either quantum or post-quantum algorithms. However, the efficiency of quantum algorithms impacts the security of the post-quantum digital signature scheme. We propose an intrusion resistant algorithm exploiting and applying quantum principles in the post-quantum signature algorithm. We use the Bennett 1992 (B92) protocol, a quantum key distribution scheme, to obtain the cipher, and the practical Stateless Hash-based Signatures (SPHINCS)-256 protocol to obtain a post-quantum signature. However, instead of Chacha-12, a well-known cryptographically secure pseudo-random number generator, we apply a quantum random number generator to obtain a truly random Hash to Obtain Random Subset (HORS) signature with Tree (HORST) secret key used in SPHINCS-256. We have implemented the design in Python with the Quantum Information Toolkit. We have validated the proposed algorithm using the Probabilistic Model Checking for Performance and Reliability Analysis (PRISM) and Scyther tools. Moreover, the National Institute of Standards and Technology (NIST) statistical tests show that the proposed algorithm key pairs have randomness of 98% and RSA and ECDSA are below 96%.

Key-Size-Driven Wavelength Resource Sharing Scheme for QKD and the Time-Varying Data Services

Integrating quantum key distribution (QKD) into the optical network through wavelength division multiplex (WDM) is promising for establishing large-scale QKD networks. However, the existing wavelength assignment schemes for WDM-QKD network all require to reserve a dedicate waveband for quantum signals, which influences the provisioning of data services, especially when the resource is tight. In this article, considering the quantum key pool (QKP) technology in the current QKD network, we propose a flexible key-size-driven wavelength assignment (KSD-WA) scheme to recycle the wavelength fragment to transmit quantum signals. Additionally, considering the noise impacts and the limited reconfiguration operations, we propose a heuristic algorithm to optimize the fragment selection with the objective of maximizing the secure key rate in the dynamic scenario. We also design a deep reinforcement learning (DeepRL) based algorithm to automatically learn the optimization policy under different environments. The simulation results verify that comparing with the conventional fixed-band (FB) scheme, the KSD-WA scheme assisted by the proposed optimization algorithms can provide adequate keys for encryption without affecting the provisioning of coexisting data services, which improves the compatibility of QKD with the real-life optical networks.

Integrating deep learning to achieve phase compensation for free-space orbital-angular-momentum-encoded quantum key distribution under atmospheric turbulence

A high-dimensional quantum key distribution (QKD), which adopts degrees of freedom of the orbital angular momentum (OAM) states, is beneficial to realize secure and high-speed QKD. However, the helical phase of a vortex beam that carries OAM is sensitive to the atmospheric turbulence and easily distorted. In this paper, an adaptive compensation method using deep learning technology is developed to improve the performance of OAM-encoded QKD schemes. A convolutional neural network model is first trained to learn the mapping relationship of intensity profiles of inputs and the turbulent phase, and such mapping is used as feedback to control a spatial light modulator to generate a phase screen to correct the distorted vortex beam. Then an OAM-encoded QKD scheme with the capability of real-time phase correction is designed, in which the compensation module only needs to extract the intensity distributions of the Gaussian probe beam and thus ensures that the information encoded on OAM states would not be eavesdropped. The results show that our method can efficiently improve the mode purity of the encoded OAM states and extend the secure distance for the involved QKD protocols in the free-space channel, which is not limited to any specific QKD protocol.

Optical preamplifier based simultaneous quantum key distribution and classical communication scheme

That the simultaneous quantum key distribution and classical communication (SQCC) scheme are combined with the continuous variable quantum key distribution (CVQKD) and the classical communication together, will provide an effective method to implement the simultaneous CVQKD and the classical communication in the existing optical networks in the future. However, superimposing a classical signal on the quantum signal will introduce excess noise into the CVQKD system, thus greatly reducing the performance of the system. In this paper, a novel scheme of SQCC based on optical preamplifier (OPA) is proposed, that is, the OPA is inserted into the receiver to improve the performance of the system. On the one hand, under the condition of the same bit error rate, the amplification of the signal by the OPA can reduce the requirement for the modulation amplitude of the classical signal at the sending end, thereby reducing the noise effect of the classical signal on the quantum signal. On the other hand, the OPA can compensate for the imperfection of the receiver detector. Moreover, in the case of locally generated local oscillator, the amplifier can also amplify the weak phase reference pulse, and thus reducing the phase excess noise caused by the shot noise of the weak phase reference pulse. Numerical simulation results show that the proposed scheme has better performance than the original scheme in the sense of security key rate and transmission distance. These results show that this scheme provides an effective and practical method for the further development and practical application of the SQCC scheme.

Quantum Key Distribution Secured Optical Networks: A Survey

Increasing incidents of cyber attacks and evolution of quantum computing poses challenges to secure existing information and communication technologies infrastructure. In recent years, quantum key distribution (QKD) is being extensively researched, and is widely accepted as a promising technology to realize secure networks. Optical fiber networks carry a huge amount of information, and are widely deployed around the world in the backbone terrestrial, submarine, metro, and access networks. Thus, instead of using separate dark fibers for quantum communication, integration of QKD with the existing classical optical networks has been proposed as a cost-efficient solution, however, this integration introduces new research challenges. In this paper, we do a comprehensive survey of the state-of-the-art QKD secured optical networks, which is going to shape communication networks in the coming decades. We elucidate the methods and protocols used in QKD secured optical networks, and describe the process of key establishment. Various methods proposed in the literature to address the networking challenges in QKD secured optical networks, specifically, routing, wavelength and time-slot allocation (RWTA), resiliency, trusted repeater node (TRN) placement, QKD for multicast service, and quantum key recycling are described and compared in detail. This survey begins with the introduction to QKD and its advantages over conventional encryption methods. Thereafter, an overview of QKD is given including quantum bits, basic QKD system, QKD schemes and protocol families along with the detailed description of QKD process based on the Bennett and Brassard-84 (BB84) protocol as it is the most widely used QKD protocol in the literature. QKD system are also prone to some specific types of attacks, hence, we describe the types of quantum hacking attacks on the QKD system along with the methods used to prevent them. Subsequently, the process of point-to-point mechanism of QKD over an optical fiber link is described in detail using the BB84 protocol. Different architectures of QKD secured optical networks are described next. Finally, major findings from this comprehensive survey are summarized with highlighting open issues and challenges in QKD secured optical networks.

Reliability and Security Analysis of an Entanglement-Based QKD Protocol in a Dynamic Ground-to-UAV FSO Communications System

Quantum cryptography is a promising technology that achieves unconditional security, which is essential to a wide range of sensitive applications. In contrast to optical fiber, the free-space optical (FSO) link is efficiently used as a quantum channel without affecting the polarization of transmitted photons. However, the FSO link has several impairments, such as atmospheric turbulence and pointing errors, which affect the performance of the quantum channel. This paper proposes a quantum key distribution (QKD) scheme that uses a time-bin entanglement protocol over the FSO channel that suffers from various channel impairments. Due to the interest in unmanned aerial vehicles (UAVs) and their usefulness for many social, internet-of-things (IoT), civil, and military applications, the proposed QKD-FSO system is integrated with the ground-to-UAV platform. Furthermore, variances in the position and orientation of the UAV are investigated using a tracking system. These variances are considered when evaluating the overall performance of the proposed integrated system. For this purpose, closed-form expressions are obtained for the system average symbol error rate (ASER) and outage probability. The Monte Carlo simulation is used to verify the validity of the proposed expressions. The system security is investigated assuming photon number splitting (PNS) attack. Moreover, the transmit power, time-bin number, and modulation order are optimized to maximize the raw and secret key rates. The results show that for 500 m link, ASER < 10-1 and link outage probability < 10-1 with tolerating boresight displacement up to 30 cm, the system should be configured at receiver’s field-of-view > 22 mrad and signal-to-noise ratio > 7.5 dB which leads SNRth < 2.5 dB and raw key rate maximized by adjusting the number of time bins according to the received SNR.

Optimal photon pairs for quantum communication protocols

We theoretically investigate the problem of finding optimal characteristics of photon pairs, produced in the spontaneous parametric down-conversion (SPDC) process, for fiber-based quantum communication protocols. By using the accessible setup parameters, the pump pulse duration and the extended phase-matching function width, we minimize the temporal width of SPDC photons within the general scenario. This allows one to perform more effectively the temporal filtering procedure, which aims at reducing the noise acquired by the measurement devices. Moreover, we compare the obtained results with the achievable parameter values for SPDC sources based on beta-Barium Borate crystal. We also investigate the influence of non-zero detection timing jitter. Finally, we apply our optimization strategy to a simple quantum key distribution scheme to show that the full optimization of an SPDC source can potentially extend the maximal security distance by several tens of kilometres, which is around 30% more as compared to previous approaches.

Quantum key distribution over free space optic (FSO) channel using higherorder Gaussian beam spatial modes

Quantum key distribution(QKD) has emerged as a secure solution of secret key distribution utilizing the well established theories of modern physics. Since its introduction in 1984, many interesting and innovative ideas have been proposed for QKD in order to improve the security and efficiency of the scheme keeping in view of its applications and practicalimplementation. High error rate QKD scheme for long distance communication-theso-called KMB09 protocol is one such scheme which was designed to achieve longer communication distance in QKD, without compromising its security,by allowing the utilisation of higher dimensional photon states which is not possible with standard BB84 scheme. However the practical implementation of KMB09 protocol has not been presented yet because of its unique design. In this paper, we propose a framework for the practical implementation of QKD system that runs KMB09 protocol in two or more dimensions of photon states. We present the KMB09 based QKD system design and its simulation for practical implementation based on the encoding of secret bits in higher order Gaussian beam spatial modes. The proposed framework is specifically evaluated in terms of efficiency or success rate with two and four dimensions of photon states. We find that the simulation results of the proposed framework are inline with the numerical and analytical results of the same QKD model presented earlier.

Multi-hop quantum key distribution with passive relays over underwater turbulence channels

Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In this paper, as a potential solution to overcome range limitations, we investigate a multi-hop underwater quantum key distribution (QKD) where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays that simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of a relay-assisted QKD scheme in terms of quantum bit error rate and secret key rate in different water types and turbulence conditions. We further investigate the effect of system parameters such as aperture size and detector field of view on the performance. Our results demonstrate under what conditions relay-assisted QKD can be beneficial and what end-to-end transmission distances can be supported with a multi-hop underwater QKD system.

Continuous variable B92 quantum key distribution protocol using single photon added and subtracted coherent states

In this paper, a continuous variable B92 quantum key distribution (QKD) protocol is proposed using single photon added and subtracted coherent states, which are prepared by adding and subsequently subtracting a single photon on a coherent state. It is established that in contrast to the traditional discrete variable B92 protocol, this protocol for QKD is intrinsically robust against the unambiguous state discrimination attack, which circumvents the requirement for any uninformative states or entanglement used in corresponding discrete variable case as a remedy for this attack. Further, it is shown that the proposed protocol is intrinsically robust against the eavesdropping strategies exploiting classical communication during basis reconciliation, such as beam splitter attack. Security against some individual attacks, key rate, and bit-error rate estimation for the proposed scheme are also provided. Specifically, the proposed scheme ensures very small bit-error rate due to properties of the states used. Thus, the proposed scheme is shown to be preferable over the corresponding discrete variable B92 protocol as well as some similar continuous variable quantum key distribution schemes.

Chaotic Quantum Key Distribution

The ability to send information securely is a vital aspect of today’s society, and with the developments in quantum computing, new ways to communicate have to be researched. We explored a novel application of quantum key distribution (QKD) and synchronized chaos which was utilized to mask a transmitted message. This communication scheme is not hampered by the ability to send single photons and consequently is not vulnerable to number splitting attacks like other QKD schemes that rely on single photon emission. This was shown by an eavesdropper gaining a maximum amount of information on the key during the first setup and listening to the key reconciliation to gain more information. We proved that there is a maximum amount of information an eavesdropper can gain during the communication, and this is insufficient to decode the message.

Performance Improvement of Discretely Modulated Continuous-Variable Quantum Key Distribution with Untrusted Source via Heralded Hybrid Linear Amplifier

In practical quantum communication networks, the scheme of continuous-variable quantum key distribution (CVQKD) faces a challenge that the entangled source is controlled by a malicious eavesdropper, and although it still can generate a positive key rate and security, its performance needs to be improved, especially in secret key rate and maximum transmission distance. In this paper, we proposed a method based on the four-state discrete modulation and a heralded hybrid linear amplifier to enhance the performance of CVQKD where the entangled source originates from malicious eavesdropper. The four-state CVQKD encodes information by nonorthogonal coherent states in phase space. It has better transmission distance than Gaussian modulation counterpart, especially at low signal-to-noise ratio (SNR). Moreover, the hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can improve the probability of amplification success and reduce the noise penalty caused by the measurement. Furthermore, the hybrid linear amplifier can raise the SNR of CVQKD and tune between two types of performance for high-gain mode and high noise-reduction mode, therefore it can extend the maximal transmission distance while the entangled source is untrusted.

Multi-label learning for improving discretely-modulated continuous-variable quantum key distribution

We propose a novel scheme for discretely-modulated continuous-variable quantum key distribution (CVQKD) using machine learning technologies, which called multi-label learning-based CVQKD (ML-CVQKD). In particular, the proposed scheme divides the whole quantum system into state learning process and state prediction process. The former is used for training and estimating classifier, and the latter is used for generating final secret key. Meanwhile, a multi-label classification algorithm (MLCA) is also designed as an embedded classifier for distinguishing coherent state. Feature extraction for coherent state and related machine learning-based metrics for the quantum classifier are successively suggested. Security analysis based on the linear bosonic channel assumption shows that MLCA-embedded ML-CVQKD outperforms other existing discretely-modulated CVQKD protocols, such as four-state protocol and eight-state protocol, as well as the original Gaussian-modulated CVQKD protocol, and it will be further enhanced with the increase of modulation variance.

Lightweight group key distribution schemes based on pre‐shared pairwise keys

In a secure communication, a one-time session key is needed to be shared among all participants. Most well-known key distribution schemes, such as Diffie–Hellman public-key key distribution scheme invented in 1976 and quantum key distribution scheme invented in 1984 (also called the BB84 scheme), can only allow two users to share a key in conventional one-to-one communications. There are many research papers in the literature to propose group key distribution schemes for multiple participants in modern group communications. In this study, the authors propose lightweight group key distributions using pre-shared pairwise keys. The authors first propose a three-party group key distribution scheme. They then extend the basic three-party scheme to establish a group key for a large size of group communications. The proposed generalised schemes can be based to any type of pairwise key distribution schemes, e.g. either quantum or non-quantum. Moreover, both generalised multi-party group key distribution schemes are lightweight. The main operations in the proposed schemes are key comparison between two or more than two keys (i.e. logic XOR operation) and the computation of key derivation functions.

Efficient Time-Bin Encoding for Practical High-Dimensional Quantum Key Distribution

High-dimensional quantum key distribution (QKD) allows achievement of information-theoretic secure communications, providing high key-generation rates, which cannot, in principle, be obtained by QKD protocols with binary encoding. Nonetheless, the amount of experimental resources needed increases as the quantum states to be detected belong to a larger Hilbert space, thus raising the costs of practical high-dimensional systems. Here, we present an alternative scheme for fiber-based four-dimensional QKD, with time and phase encoding and one-decoy state technique. Quantum state transmission is tested over different channel lengths up to 145 km of standard single-mode fiber, evaluating the enhancement of the secret key rate in comparison to the three-state two-dimensional BB84 protocol, which is tested with the same experimental setup. Our scheme allows measurement of the four-dimensional states with a simplified and compact receiver, where only two single-photon detectors are necessary, thus making it a cost-effective solution for practical and fiber-based QKD.

Emulation of up-conversion based quantum key distribution scheme using active pump-controlled basis selection and adaptive thresholding

We emulate a method for quantum key distribution (QKD) that employs up-conversion detection. The scheme uses differential quadrature phase shift modulation and actively chooses the measurement basis by applying a dynamic phase-shift on the pump of the up-conversion interaction. The QKD rate of the quantum-hacking resistant system over an emulated 7.5 km marine-like turbulent channel is evaluated including the impact of thresholding the received data so as to ignore signals that are below a tolerable signal-to-noise ratio. The emulated system is well suited to operate over marine free space optical links coupled to single mode fiber.

An entanglement-based quantum network based on symmetric dispersive optics quantum key distribution

Quantum key distribution (QKD) is a crucial technology for information security in the future. Developing simple and efficient ways to establish QKD among multiple users is important to extend the applications of QKD in communication networks. Herein, we proposed a scheme of symmetric dispersive optics QKD and demonstrated an entanglement-based quantum network based on it. In the experiment, a broadband entangled photon pair source was shared by end users via wavelength and space division multiplexing. The wide spectrum of generated entangled photon pairs was divided into 16 combinations of frequency-conjugate channels. Photon pairs in each channel combination supported a fully connected subnet with eight users by a passive beam splitter. Eventually, it showed that an entanglement-based QKD network over 100 users could be supported by one entangled photon pair source in this architecture. It has great potential on applications of local quantum networks with large user number.

Photon Subtraction-Induced Plug-and-Play Scheme for Enhancing Continuous-Variable Quantum Key Distribution with Discrete Modulation

Establishing high-rate secure communications is a potential application of continuous-variable quantum key distribution (CVQKD) but still challenging for the long-distance transmission technology compatible with modern optical communication systems. Here, we propose a photon subtraction-induced plug-and-play scheme for enhancing CVQKD with discrete-modulation (DM), avoiding the traditional loopholes opened by the transmission of local oscillator. A photon subtraction operation is involved in the plug-and-play scheme for detection while resisting the extra untrusted source noise of the DM-CVQKD system. We analyze the relationship between secret key rate, channel losses, and untrusted source noise. The simulation result shows that the photon-subtracted scheme enhances the performance in terms of the maximal transmission distance and make up for the deficiency of the original system effectively. Furthermore, we demonstrate the influence of finite-size effect on the secret key rate which is close to the practical implementation.

Symmetry-Protected Privacy: Beating the Rate-Distance Linear Bound Over a Noisy Channel

There are two main factors limiting the performance of quantum key distribution---channel transmission loss and noise. Previously, a linear bound was believed to put an upper limit on the rate-transmittance performance. Remarkably, the recently proposed twin-field and phase-matching quantum key distribution schemes have been proven to overcome the linear bound. In practice, due to the intractable phase fluctuation of optical signals in transmission, these schemes suffer from large error rates, which renders the experimental realization extremely challenging. Here, we close this gap by proving the security based on a different principle---encoding symmetry. With the symmetry-based security proof technique, we can decouple the privacy from the channel disturbance, and eventually remove the limitation of secure key distribution on bit error rates. As a direct application, we show that the phase-matching scheme can yield positive key rates even with high bit error rates up to 50%. In the simulation, with typical experimental parameters, the key rate is able to break the linear bound with an error rate of 13%. Meanwhile, we provide a simple finite-data size analysis for the phase-matching scheme under this symmetry-based analysis, which can break the bound with a reasonable data size of ${10}^{12}$. Encouraged by high loss and error tolerance, we expect the approach based on symmetry-protected privacy will provide a different insight into the security of quantum key distribution.