Secure Key Generation Rate Research Articles

Wireless-Channel Key Distribution Based on Laser Synchronization.

We propose and experimentally demonstrate a wireless-channel key distribution scheme based on laser synchronization induced by a common wireless random signal. Two semiconductor lasers are synchronized under injection of the drive signal after electrical-optical conversion and emit irregular outputs that are used to generate shared keys. Our proof-of-concept experiment using a complex drive signal achieved a secure key generation rate of up to 150 Mbit/s with a bit error rate below 3.8 × 10-3. Numerical simulation results show that the proposed scheme has the potential to achieve a distribution distance of several hundred meters. It is believed that common-signal-induced laser synchronization paves the way for high-speed wireless physical-layer key distribution.

Theoretical analysis of quantum key distribution systems when integrated with a DWDM optical transport network

Theoretical research and numerical simulation of the noise influence caused by spontaneous Raman scattering, four-wave mixing, and linear channel cross talk on the performances of quantum key distribution (QKD) systems were conducted. Three types of QKD systems were considered: a coherent one-way QKD protocol, subcarrier-wave QKD system, and continuous-variable QKD integrated with classical dense wavelength division multiplexing (DWDM) channels. We calculate the secure key generation rate for the systems mentioned addressing different channel allocation schemes (i.e., configurations). A uniform DWDM grid is considered with a quantum channel located in the C-band and O-band (at 1310 nm) of a telecommunication window. The systems’ performances are analyzed in terms of the maximal achievable distance values. Configurations for further analysis and investigation are chosen optimally, i.e., their maximal achievable distances are the best.

Performance analysis of continuous-variable quantum key distribution using non-Gaussian states

In this study, we analyze the efficiency of a protocol with discrete modulation of continuous variable non-Gaussian states, the coherent states having one photon added and then one photon subtracted (PASCS). We calculate the secure key generation rate against collective attacks using the fact that Eve's information can be bounded based on the protocol with Gaussian modulation, which in turn is unconditionally secure. Our results for a four-state protocol show that the PASCS always outperforms the equivalent coherent states protocol under the same environmental conditions. Interestingly, we find that for the protocol using discrete-modulated PASCS, the noisier the line, the better will be its performance compared to the protocol using coherent states. Thus, our proposal proves to be advantageous for performing quantum key distribution in non-ideal situations.

Theoretical analysis of measurement-device-independent quantum key distribution systems integrated into fiber-optic communication lines using dense wavelength division multiplexing

Subject of study. The effect of noise resulting from spontaneous Raman scattering, four-wave mixing, and linear channel crosstalk on the performance of measurement-device-independent quantum key distribution systems with symmetric and asymmetric realizations is studied. Mathematical models of the measurement-device-independent quantum key distribution system and considered channel noise sources are presented. The secure key generation rate was calculated in all cases for assessment and subsequent analysis of the system performance. These results enabled the identification and presentation of the operation features of the measurement-device-independent quantum key distribution system upon its integration into existing fiber-optic communication networks using dense wavelength division multiplexing. Aim of the work. The performance of measurement-device-independent quantum key distribution systems integrated into fiber-optic communication lines using dense wavelength division multiplexing by means of numerical simulation is investigated. Method. An approach based on analysis of the Raman scattering cross section plot and allocation of the information channels of frequencies corresponding to areas located sideways to the pump wavelength was used to determine the optimal configurations of the allocation of quantum and information channels. A single-photon scheme in one symmetric and two asymmetric system realizations was considered for numerical simulations of the quantum key distribution system with an untrusted node. A security analysis was performed according to the Devetak–Winter bound that enables estimating the secure key generation rate in an asymptotic mode (for symmetric infinite sequences) in the presence of collective attacks in the quantum channel. Main results. It was confirmed that the implementation of measurement-device-independent quantum key distribution systems with equal paths of the sender and the receiver (i.e., symmetric) is optimal. The result deteriorated with an increase in the asymmetry parameter. If the quantum channel is within the C-band, the advantage of the symmetric realization was minimal, and it was almost indiscernible when the number of information channels was increased to 40. However, if the quantum channel was at the wavelength of 1310 nm (O band), the difference was significant. Moreover, allocation of the wavelength of 1310 nm to the quantum channel enables the longest distance of operation, and it weakly depends on the number of channels. Practical significance. For practical implementation of quantum key distribution systems, their integration into existing telecommunication infrastructure is of particular interest. This can be achieved through the simultaneous propagation of quantum and information channels in the fiber-optic communication lines by means of multiplexing, and in particular, dense wavelength division multiplexing. However, the power levels characteristic for quantum signals are significantly lower than those for information signals. Therefore, if the information and quantum channels propagate in the same fiber, the noise from the information channels significantly reduces the performance of the quantum key distribution systems. For this reason, the physical and mathematical description, analysis, and numerical simulation of the noise and its interaction with different quantum key distribution systems aimed at identifying the most effective integration method are crucial for the integration of quantum key distribution systems into existing telecommunication networks.

A theoretical study of subcarrier-wave quantum key distribution system integration with an optical transport network utilizing dense wavelength division multiplexing

In this paper we study the performance of subcarrier-wave quantum key distribution (SCW QKD) in the presence of classical channels of optical transport network utilizing dense wavelength division multiplexing (DWDM). We consider the impact of spontaneous Raman scattering noise as well as the four-wave mixing and channel isolation efficiency. We calculate quantum bit error rate as well as the secure key generation rate of SCW-QKD protocol for different parameters of DWDM system and quantum channel allocations. Our calculations show, that quantum channel allocation at the wavelength of 1310 nm is preferable to allocation at C-band due to lower nonlinear noise, despite fiber’s larger attenuation at this wavelength.

Performance of subcarrier-wave quantum key distribution in the presence of spontaneous Raman scattering noise generated by classical DWDM channels

In this paper, we study the performance of the subcarrier-wave quantum key distribution system (SCW QKD) in the presence of spontaneous Raman scattering (SpRS) noise generated by classical channels of the dense wavelength division multiplexing (DWDM) network within a single-mode optical fiber. We present the mathematical model for evaluation of the quantum bit error rate and secure key generation rate with the SpRS noise taken into account. We consider two regimes of the SCW QKD system: the continuous wave regime, which uses a continuous wave laser, and the pulsed regime. For these regimes, performance of the system is analyzed depending on receiver sensitivity of classical DWDM. It is found that the pulsed regime outperforms the continuous wave regime in both the secure key generation rate and maximum achievable distance.

High-speed and Large-scale Privacy Amplification Scheme for Quantum Key Distribution

State-of-art quantum key distribution (QKD) systems are performed with several GHz pulse rates, meanwhile privacy amplification (PA) with large scale inputs has to be performed to generate the final secure keys with quantified security. In this paper, we propose a fast Fourier transform (FFT) enhanced high-speed and large-scale (HiLS) PA scheme on commercial CPU platform without increasing dedicated computational devices. The long input weak secure key is divided into many blocks and the random seed for constructing Toeplitz matrix is shuffled to multiple sub-sequences respectively, then PA procedures are parallel implemented for all sub-key blocks with correlated sub-sequences, afterwards, the outcomes are merged as the final secure key. When the input scale is 128 Mb, our proposed HiLS PA scheme reaches 71.16 Mbps, 54.08 Mbps and 39.15 Mbps with the compression ratio equals to 0.125, 0.25 and 0.375 respectively, resulting achievable secure key generation rates close to the asymptotic limit. HiLS PA scheme can be applied to 10 GHz QKD systems with even larger input scales and the evaluated throughput is around 32.49 Mbps with the compression ratio equals to 0.125 and the input scale of 1 Gb, which is ten times larger than the previous works for QKD systems. Furthermore, with the limited computational resources, the achieved throughput of HiLS PA scheme is 0.44 Mbps with the compression ratio equals to 0.125, when the input scale equals up to 128 Gb. In theory, the PA of the randomness extraction in quantum random number generation (QRNG) is same as the PA procedure in QKD, and our work can also be efficiently performed in high-speed QRNG.

Multi-matrix error estimation and reconciliation for quantum key distribution.

Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.

Improving the Secure Key Rate and Error Tolerance of the Interferometer-Based Time-Frequency Encoding QKD System

The interferometer-based, time-frequency encoding quantum key distribution (TF-QKD) scheme is a promising way to loosen up the restrict resolution requirement for the temporal measurement in TF-QKD protocol. However, the utilization of delay interferometers in the existing schemes causes lower efficiency of the frequency measurement, so it would decrease the secure key generation rate and the error tolerance. In order to improve this imperfection, we propose two kinds of schemes, one is the pre-balance TF scheme (PB-TF), in which Alice actively adjusts the probability distributions of sending photons encoded in two bases. The other one is the non-delay interferometer based TF scheme (NDI-TF), in this scheme the signals are converted from serial to parallel before entering the interferometers which eliminates the extra loss of the frequency measurement with delay interferometers. We theoretically verify the performance improvement of both schemes and discuss their advantages under the practical application scenario. The simulation results show that both of the schemes can improve the secure key generation rate and the error tolerance, but the NDI-TF scheme has higher secure key generation rate especially in the high-dimensional encoding QKD systems. As for the low-dimensional system, the PB-TF scheme is preferred since its performance is comparable to the NDI-TF scheme but with low cost and easy to implement.

Employing covert communications-based information reconciliation and multiple spatial modes to polarization entanglement QKD

The information that is leaked to an eavesdropper during the error reconciliation phase of quantum key distribution (QKD) protocols limits the maximum bit error rate (BER) of a system. In a standard QKD protocol, parity bits are transmitted over an authenticated noiseless channel, to which Eve has access. This Letter presents the concept of using a covert classical communication channel to transmit the parity bits between Alice and Bob without Eve gaining information of the transmitted parity bits. This allows for higher secure key generation rates and operation of a QKD system in which the BER exceeds the limit of the standard protocol. This concept is then applied to a practical free-space optical system that contains multiple parallel channels, where channel loss, crosstalk, atmospheric turbulence effects, and noise are considered.

Fundamental limit and trade-off between security and secure key generation rate in quantum key distribution

Fundamental limit and trade-off between security and secure key generation rate in quantum key distribution

Optimized channel allocation scheme for jointly reducing four-wave mixing and Raman scattering in the DWDM-QKD system.

Conducting quantum key distribution (QKD) through existing optical fibers together with conventional communication signals is a viable way to expand its practical application, but weak quantum signals can be severely disrupted by co-propagating classical signals. In this paper, the suppression of four-wave mixing (FWM) noise and Raman noise is considered simultaneously for the first time, to the best of our knowledge, and the joint optimized channel allocation (JOCA) scheme is proposed. In the JOCA scheme, the quantum channels and classical channels are interleaved with each other to avoid FWM noise and optimal quantum channel positions are chosen in variable conditions according to the Raman scattering spectrum. Experimental measurements of the noise photons show that the JOCA scheme can effectively reduce the impairments on quantum signals compared with the single-target schemes. Additionally, simulation results verify that the JOCA scheme can increase the secure key generation rate and transmission distance, and that it also enables the DWDM-QKD system to tolerate higher-power classical signals and more classical channels, which improve the compatibility with a high-capacity communication system.

Quantum key distribution using in-line highly birefringent interferometers

Secure communication networks enabled by commercial quantum key distribution (QKD) are already available. However, their widespread deployment will require great efforts towards reducing the currently prohibitive cost of QKD systems. Here, we propose a compact and cost-effective alternative to the asymmetric Mach-Zehnder interferometer commonly used to implement phase encoding in the Bennett-Brassard 1984 (BB84) QKD protocol. Our solution consists of an all-fiber, in-line, highly birefringent interferometer (HBI). The HBI shows improved tolerance to length mismatches and a simpler assembly, making it particularly desirable for the fabrication of multi-user systems where several interferometers must have matched delays and where cost and space considerations can be most critical, such as quantum access networks. As a proof-of-principle, we demonstrate point-to-point QKD operation with HBIs over 15.5 km drop fiber and an 8-port passive optical network splitter. We achieve a secure key generation rate of 299.4 ± 16.4 kbit/s with a quantum bit error rate of 2.89 ± 0.31% for a continuous 25 h operation period.

Social-Aware Secret Key Generation for Secure Device-to-Device Communication via Trusted and Non-Trusted Relays

Physical layer security (PLS) is a promising technology in device-to-device (D2D) communications by exploiting reciprocity and randomness of wireless channels, which attracts considerable research attention in the D2D communications community. In this paper, we investigated PLS for secure key generation rate (SKGR) in D2D communications based on cooperative trusted and non-trusted relays. By leveraging social ties, we exploit three social phenomena for secure communications, i.e., trusted scenario (social trust), non-trusted scenario (social reciprocity), and partially trusted scenario (mixed social trust and social reciprocity). The coalition game theory is further utilized to select the optimal relay pairs for improving SKGR. On the basis of social ties, we develop an algorithm for SKGR that protects the keys secret from both eavesdropper and non-trusted selected relays. We incorporate secure relays selection and system wide security for D2D communications. The stability and convergence of the proposed algorithm are also proved in this paper. Both numerical and analytical results verify effectiveness and consistency of our proposed scheme, which ensures better SKGR performance in D2D communications.

Phase-encoded measurement device independent quantum key distribution without a shared reference frame

In this paper, a phase-encoded measurement device independent quantum key distribution (MDI-QKD) protocol without a shared reference frame is presented, which can generate secure keys between two parties while the quantum channel or interferometer introduces an unknown and slowly time-varying phase. The corresponding secret key rate and single photons bit error rate is analysed, respectively, with single photons source (SPS) and weak coherent source (WCS), taking finite-key analysis into account. The numerical simulations show that the modified phase-encoded MDI-QKD protocol has apparent superiority both in maximal secure transmission distance and key generation rate while possessing the improved robustness and practical security in the high-speed case. Moreover, the rejection of the frame-calibrating part will intrinsically reduce the consumption of resources as well as the potential security flaws of practical MDI-QKD systems.

Modeling satellite-Earth quantum channel downlinks with adaptive-optics coupling to single-mode fibers

The efficient coupling of photons from a free-space quantum channel into a single-mode optical fiber (SMF) has important implications for quantum network concepts involving SMF interfaces to quantum detectors, atomic systems, integrated photonics, and direct coupling to a fiber network. Propagation through atmospheric turbulence, however, leads to wavefront errors that degrade mode matching with SMFs. In a free-space quantum channel, this leads to photon losses in proportion to the severity of the aberration. This is particularly problematic for satellite-Earth quantum channels, where atmospheric turbulence can lead to significant wavefront errors. This report considers propagation from low-Earth orbit to a terrestrial ground station and evaluates the efficiency with which photons couple either through a circular field stop or into an SMF situated in the focal plane of the optical receiver. The effects of atmospheric turbulence on the quantum channel are calculated numerically and quantified through the quantum bit error rate and secure key generation rates in a decoy-state BB84 protocol. Numerical simulations include the statistical nature of Kolmogorov turbulence, sky radiance, and an adaptive-optics system under closed-loop control.

Secure detection in quantum key distribution by real-time calibration of receiver

The single-photon detectionefficiency of the detector unit is crucial for the security of common quantum key distribution protocols like Bennett-Brassard 1984 (BB84). A low value for the efficiency indicates a possible eavesdropping attack that exploits the photon receiver’s imperfections. We present a method for estimating the detection efficiency, and calculate the corresponding secure key generation rate. The estimation is done by testing gated detectors using a randomly activated photon source inside the receiver unit. This estimate gives a secure rate for any detector with non-unity single-photon detection efficiency, both inherit or due to blinding. By adding extra optical components to the receiver, we make sure that the key is extracted from photon states for which our estimate is valid. The result is a quantum key distribution scheme that is secure against any attack that exploits detector imperfections.

Error Rate Estimation in Quantum Key Distribution with Finite Resources**Supported by the National Natural Science Foundation of China under Grant Nos. U1304613 and 11204379

The goal of quantum key distribution (QKD) is to generate secret key shared between two distant players, Alice and Bob. We present the connection between sampling rate and erroneous judgment probability when estimating error rate with random sampling method, and propose a method to compute optimal sampling rate, which can maximize final secure key generation rate. These results can be applied to choose the optimal sampling rate and improve the performance of QKD system with finite resources.

Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver

Spatial filtering is an important technique for reducing sky background noise in a satellite quantum key distribution downlink receiver. Atmospheric turbulence limits the extent to which spatial filtering can reduce sky noise without introducing signal losses. Using atmospheric propagation and compensation simulations, the potential benefit of adaptive optics (AO) to secure key generation (SKG) is quantified. Simulations are performed assuming optical propagation from a low-Earth-orbit satellite to a terrestrial receiver that includes AO. Higher-order AO correction is modeled assuming a Shack–Hartmann wavefront sensor and a continuous-face-sheet deformable mirror. The effects of atmospheric turbulence, tracking, and higher-order AO on the photon capture efficiency are simulated using statistical representations of turbulence and a time-domain wave-optics hardware emulator. SKG rates are calculated for a decoy-state protocol as a function of the receiver field of view for various strengths of turbulence, sky radiances, and pointing angles. The results show that at fields of view smaller than those discussed by others, AO technologies can enhance SKG rates in daylight and enable SKG where it would otherwise be prohibited as a consequence of background optical noise and signal loss due to propagation and turbulence effects.

Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions

Nonorthogonal coded agreements and decoy state method can effectively protect the photon number against splitting attack. Owing to the fact that the component of single-photon in the coherent-state superposition (CSS) is as high as 90%, CSS has recently emerged as an alternative to single-photon qubits for quantum information processing and metrology. The approximate CSS of small amplitudes is generated by the subtraction of photons from a squeezed vacuum state, and the approximate CSS of large amplitude is generated from Fock state by using a single homodyne detection. Here, we combine both of the methods and propose a new protocol by using the CSS as a light source. We derive the secure key generation rate, the lower bound of count rate and upper bound of error rate of single-photon. We simulate the curves relationship between secure key generation rate and safety transmission distance in the case of an infinite number of decoy states by using matlab. The parameters are given according to the Gobby-Yuan-Shields (GYS) experiment. We infer that the safety transmission distance achieves 147.4 km and the secure key generation rate is much higher than those of other schemes. We also simulate the relationship between key generation rate and safety transmission distance in the case of a limited number of decoy states by using matlab. The parameters are given according to the GYS experiment too. When the N is 1010, the safety transmission distance achieves 144 km; when the N is 109, the safety transmission distance achieves 139 km; when the N is 108, the safety transmission distance achieves 125.9 km. In this paper, we propose the use of CSS as the light source. Combining SARG04 agreements and decoy state, the scheme has the following advantages: first, the scheme which combines SARG04 agreements and decoy state method can effectively resist PNS; second, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions has a longer safety transmission distance and higher secure key generation rate than nonorthogonal decoy-state quantum key distribution based on weak coherent pulse and nonorthogonal decoy-state quantum key distribution based on conditionally prepared down-conversion source; third, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions is easier to prepare, which just needs one decoy state, than other schemes that require several decoy states. Obviously, our scheme can enhance the performance of quantum key distribution. Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions will have a very good application with the further development of preparation technology of CSS.