Quantum Bit Error Rate Research Articles

The statistical fluctuation study of quantum key distribution in means of uncertainty principle

Laser defects in emitting single photon, photon signal attenuation and propagation of error cause our serious headaches in practical long-distance quantum key distribution (QKD) experiment for a long time. In this paper, we study the uncertainty principle in metrology and use this tool to analyze the statistical fluctuation of the number of received single photons, the yield of single photons and quantum bit error rate (QBER). After that we calculate the error between measured value and real value of every parameter, and concern the propagation error among all the measure values. We paraphrase the Gottesman–Lo–Lutkenhaus–Preskill (GLLP) formula in consideration of those parameters and generate the QKD simulation result. In this study, with the increase in coding photon length, the safe distribution distance is longer and longer. When the coding photon’s length is $$N = 10^{11}$$ , the safe distribution distance can be almost 118 km. It gives a lower bound of safe transmission distance than without uncertainty principle’s 127 km. So our study is in line with established theory, but we make it more realistic.

Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective

We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity. Specifically, from our simulation results, the threshold probability of the QBER curves for the color codes, rotated-surface codes, surface codes, and toric codes are given by $1.8 \times 10^{-2}$ , $1.3 \times 10^{-2}$ , $6.3 \times 10^{-2}$ , and $6.8 \times 10^{-2}$ , respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97, and 0.99 by employing the 1/7-rate color code, the 1/9-rate rotated-surface code, and 1/13-rate surface code, respectively.

Performance optimization for quantum key distribution in lossy channel using entangled photons**Project supported by the National Natural Science Foundation of China (Grant Nos. 61573059, 61401340, and 61172138), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2016JM6035), and the Fundamental Research Funds for the Central Universities, China (Grant No. JB161303).

In quantum key distribution (QKD), the times of arrival of single photons are important for the keys extraction and time synchronization. The time-of-arrival (TOA) accuracy can affect the quantum bit error rate (QBER) and the final key rate. To achieve a higher accuracy and a better QKD performance, different from designing more complicated hardware circuits, we present a scheme that uses the mean TOA of M frequency-entangled photons to replace the TOA of a single photon. Moreover, to address the problem that the entanglement property is usually sensitive to the photon loss in practice, we further propose two schemes, which adopt partially entangled photons and grouping-entangled photons, respectively. In addition, we compare the effects of these three alternative schemes on the QKD performance and discuss the selection strategy for the optimal scheme in detail. The simulation results show that the proposed schemes can improve the QKD performance compared to the conventional single-photon scheme obviously, which demonstrate the effectiveness of the proposed schemes.

A Novel Error Correction Scheme In Quantum Key Distribution (Qkd) Protocol

Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. Adopting this classical error correcting code, an improved reconciliation scheme namely Siao Ping 1985 (SP 1985) protocol is proposed in this paper to correct more errors in faster pace without additional formulation for the overall simplicity criterion. This research is aimed at building up efficiency and effectiveness of reconciliation of the robust BB84 protocol in coping with noise interference. The proposed SP 1985 reconciliation protocol utilizes a pair of forward and reverse order syndromes for error pattern recognition. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits. Therefore, it is sufficient to deliver the desirable outcome after investigating its capability by correcting two errors out of seven bits compared to Winnow protocol. Its effectiveness can be measured based on simulation result which leads to reducing the QBER.

Critical side channel effects in random bit generation with multiple semiconductor lasers in a polarization-based quantum key distribution system.

Most polarization-based BB84 quantum key distribution (QKD) systems utilize multiple lasers to generate one of four polarization quantum states randomly. However, random bit generation with multiple lasers can potentially open critical side channels that significantly endangers the security of QKD systems. In this paper, we show unnoticed side channels of temporal disparity and intensity fluctuation, which possibly exist in the operation of multiple semiconductor laser diodes. Experimental results show that the side channels can enormously degrade security performance of QKD systems. An important system issue for the improvement of quantum bit error rate (QBER) related with laser driving condition is further addressed with experimental results.

Experimental free-space quantum key distribution with efficient error correction.

We report a 17-km free-space quantum key distribution (QKD) experiment using an engineering model of the space-bound optical transmitter and a ground station for satellite-ground QKD. The final key rate of ~ 0.5 kbps is achieved in this experiment with the quantum bit error rate (QBER) of ~ 3.4%. An efficient error correction algorithm, Turbo Code, is employed. Compared with the current error correction algorithm of Cascade, a high-efficiency error correction is realized by Turbo Code with only one-time data exchange. For a low QBER, with only one-time data exchange, the final key rates based on Turbo code are similar with Cascade. As the QBER increases, Turbo Code gives higher final key rates than Cascade. Our results experimentally demonstrate the feasibility of satellite-ground QKD and show that the efficient error correction based on Turbo Code is potentially useful for the satellite-ground quantum communication.

Numerical evidence for bound secrecy from two-way postprocessing in quantum key distribution

Bound secret information is classical information that contains secrecy but from which secrecy cannot be extracted. The existence of bound secrecy has been conjectured but is currently unproven, and in this work we provide analytical and numerical evidence for its existence. Specifically, we consider two-way post-processing protocols in prepare-and-measure quantum key distribution based on the well-known six-state signal states. In terms of the quantum bit-error rate $Q$ of the classical data, such protocols currently exist for $Q<\frac{5-\sqrt{5}}{10}\approx 27.6\%$. On the other hand, for $Q\geq\frac{1}{3}$ no such protocol can exist as the observed data is compatible with an intercept-resend attack. This leaves the interesting question of whether successful protocols exist in the interval $\frac{5-\sqrt{5}}{10}\leq Q<\frac{1}{3}$. Previous work has shown that a necessary condition for the existence of two-way post-processing protocols for distilling secret key is breaking the symmetric extendability of the underlying quantum state shared by Alice and Bob. Using this result, it has been proven that symmetric extendability can be broken up to the $27.6\%$ lower bound using the advantage distillation protocol. In this work, we first show that to break symmetric extendability it is sufficient to consider a generalized form of advantage distillation consisting of one round of post-selection by Bob on a block of his data. We then provide evidence that such generalized protocols cannot break symmetric extendability beyond $27.6\%$. We thus have evidence to believe that $27.6\%$ is an upper bound on two-way post-processing and that the interval $\frac{5-\sqrt{5}}{10}\leq Q<\frac{1}{3}$ is a domain of bound secrecy.

Polarization-basis tracking scheme for quantum key distribution using revealed sifted key bits.

The calibration of the polarization basis between the transmitter and receiver is an important task in quantum key distribution. A continuously working polarization-basis tracking scheme (PBTS) will effectively promote the efficiency of the system and reduce the potential security risk when switching between the transmission and calibration modes. Here, we proposed a single-photon level continuously working PBTS using only sifted key bits revealed during an error correction procedure, without introducing additional reference light or interrupting the transmission of quantum signals. We applied the scheme to a polarization-encoding BB84 QKD system in a 50 km fiber channel, and obtained an average quantum bit error rate (QBER) of 2.32% and a standard derivation of 0.87% during 24 h of continuous operation. The stable and relatively low QBER validates the effectiveness of the scheme.

Experimental realization of equiangular three-state quantum key distribution.

Quantum key distribution using three states in equiangular configuration combines a security threshold comparable with the one of the Bennett-Brassard 1984 protocol and a quantum bit error rate (QBER) estimation that does not need to reveal part of the key. We implement an entanglement-based version of the Renes 2004 protocol, using only passive optic elements in a linear scheme for the positive-operator valued measure (POVM), generating an asymptotic secure key rate of more than 10 kbit/s, with a mean QBER of 1.6%. We then demonstrate its security in the case of finite key and evaluate the key rate for both collective and general attacks.

Analysis on performance optimization in measurement-device-independent quantum key distribution using weak coherent states

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all detection side-channel attacks, thus when combined with the decoy-state method, it can avoid the actual security loophole caused by quasisingle- photon source simultaneously. A practical weak coherent source is used as a quasi-single-photon source in the current MDI-QKD experiments; it may contain percentage of vacuum-and multi-photon pulses. Moreover, in order to study how the performance of the threshold detector affects the quantum bit error rate (QBER), we introduce the quality factor (the ratio of the dark count rate to the detection efficiency) of the threshold detector. Here, through taking into account the weak coherent source, the quality factor of the threshold detector and the reflectivity of beam splitter, we deduce and evaluate the gain, the probability for successful Bell measurement, incorrect Bell measurement when Alice and Bob send pulses with different photon numbers which have a high probability to appear in weak coherent source, and then we obtain QBER in combination with the probabilities of different photon number states, besides, we also do some simulations. The simulations show how QBER varies with the reflectivity of beam splitter and the quality factor of the threshold detector when the average photon numbers per pulse from Alice and Bob are symmetric. Furthermore, the simulations show how QBER varies with the average photon number per pulse from Alice when average photon number per pulse from Bob is 0.1. Result shows that QBER is affected by the reflectivity of beam splitter, but QBER cannot reach the minimum value in Z basis encoding scheme when the average photon numbers per pulse from Alice and Bob are both 0.1 and the reflectivity of beam splitter is 0.5, which is different from X basis encoding and phase encoding. In addition, QBER increases with the increase of the quality factor of the threshold detector, which means that better performance of the threshold detector will reduce QBER. We show that QBER in Z basis encoding reaches the minimum value when reflectivity of beam splitter is 0.5 and there is large difference between in average photon number per pulse between two sides. In conclusion, for QBER, the effect from the reflectivity of beam splitter is equal to average photon numbers from the two arms only in X basis encoding and phase encoding. Our work will provide a reference for setting up a system with better performance.

Generalized Quantum Key Distribution for WDM Router Applications

In this paper, we study the ability of quantum networks to support both random and non-random data traffic single-photon quantum communications signals on a shared infrastructure. The effect of wave length on distance coverage with the quantum bit error rate (QBER) of a quantum key distribution (QKD) system is increasing. The results of random phase showed minimal distance coverage over non-random phase. For fluctuating amplitude of random show a change in system performance improved sending capabilities. Hence, it is found that rare fluctuations should not degrade system performance significantly, but the data sending mode has a significant effect on channel integrity.

Reduction of FWM noise in WDM-based QKD systems using interleaved and unequally spaced channels

To extensively deploy quantum key distribution (QKD) systems, copropagating with classical channels on the same fiber using wavelength division multiplexing (WDM) technology becomes a critical issue. We propose a user-based channel-interleaving WDM scheme with unequal frequency spacing (UFS-iWDM) to reduce the impairment on the quantum channels induced by four-wave mixing (FWM), and theoretically analyze its impact on quantum bit error rate (QBER). Numerical simulation results show that a UFS-iWDM can significantly reduce the FWM noise and improve QBER compared with the corresponding WDM scheme with equal frequency spacing (EFS), especially in the case of nonzero dispersion shifted fiber.

FPGA based digital phase-coding quantum key distribution system

Quantum key distribution (QKD) is a technology with the potential capability to achieve information-theoretic security. Phasecoding is an important approach to develop practical QKD systems in fiber channel. In order to improve the phase-coding modulation rate, we proposed a new digital-modulation method in this paper and constructed a compact and robust prototype of QKD system using currently available components in our lab to demonstrate the effectiveness of the method. The system was deployed in laboratory environment over a 50 km fiber and continuously operated during 87 h without manual interaction. The quantum bit error rate (QBER) of the system was stable with an average value of 3.22% and the secure key generation rate is 8.91 kbps. Although the modulation rate of the photon in the demo system was only 200 MHz, which was limited by the Faraday- Michelson interferometer (FMI) structure, the proposed method and the field programmable gate array (FPGA) based electronics scheme have a great potential for high speed QKD systems with Giga-bits/second modulation rate.

A Novel Error Correction Scheme in Quantum Key Distribution (QKD) Protocol

Ideally, in any quantum key distribution (QKD) communication system, each sifted key is expected to be received without error. However in practice, due to infeasibility of generating pure single photon and device impairment problem, some of the sifted key may experience errors. This results to the increment of quantum bit error rate (QBER) that requires error reconciliation for correcting error. The main concept in error reconciliation is very much related to the capability of correcting all errors while minimizing eavesdrop information. The quantum error correcting code such as Hamming code which used in Winnow protocol is found to be more attractive. However the Winnow protocol can only correct one error out of seven bits. In this paper, a modified Hamming encoder/decoder to improve Winnow protocol by correcting two errors out of seven bits which leads to reducing the QBER is presented. This design utilizes a pair of forward and reverse order syndromes for error pattern recognition. A new reconciliation protocol has been developed to enhance the error correcting capability in BB84 protocol. It is carried out in a simple structure which can correct up to double erroneous bits and detect four erroneous bits for each seven bits.

Modeling daytime sky access for a satellite quantum key distribution downlink

Daytime sky radiance can lead to quantum-bit-error rates (QBER) sufficiently high to preclude quantum key distribution over satellite-to-Earth downlinks. For circular orbits, sky radiance and propagation losses are both pointing-angle-dependent quantities. This dependence makes it possible to map the sky as a function of the QBER in certain protocols. Sky radiance distributions are generated by libRadtran software with aerosol values representative of summer and winter. Hemispherical maps of the QBER are created for orbit altitudes of 400 and 800 km. Sunrise-to-sunset simulations are presented for a system with commercial optical components and compared to a case employing an atomic-line spectral filter.

Countermeasure against probabilistic blinding attack in practical quantum key distribution systems**Project supported by the National Basic Research Program of China (Grant Nos. 2011CBA00200 and 2011CB921200), the National Natural Science Foundation of China (Grant Nos. 61475148, 61201239, 61205118, and 11304397), and the China Postdoctoral Science Foundation (Grant No. 2013M540514).

In a practical quantum key distribution (QKD) system, imperfect equipment, especially the single-photon detector, can be eavesdropped on by a blinding attack. However, the original blinding attack may be discovered by directly detecting the current. In this paper, we propose a probabilistic blinding attack model, where Eve probabilistically applies a blinding attack without being caught by using only an existing intuitive countermeasure. More precisely, our countermeasure solves the problem of how to define the bound in the limitation of precision of current detection, and then we prove security of the practical system by considering the current parameter. Meanwhile, we discuss the bound of the quantum bit error rate (QBER) introduced by Eve, by which Eve can acquire information without the countermeasure.

FPGA-Based Emulation of a Synchronous Phase-Coded Quantum Cryptography System

We present FPGA-based emulation of a synchronous phase-coded quantum cryptography system. Several of the emulated subsystems are used for implementation in a free space demonstrative QPSK scheme for quantum key distribution with continuous variables (CV-QKD) using a base and optical phase synchronization. The CV-QKD systems are commonly implemented using QPSK modulation with switched or simultaneous detection. In this paper we only make use of one base of the QPSK system in order to get a simpler modulation (BPSK) scheme, used for demonstrative purposes. The reported results from the emulation and the experiment in terms of Quantum Bit Error Rate (QBER) and mutual information for different values of the number of photons per bit are in good agreement.

Performance analysis of quantum key distribution based on air-water channel

Considering the air-water interface and ocean water’s optical attenuation, the performance of quantum key distribution (QKD) based on air-water channel is studied. The effects of photons’ various incident angles to air-water interface on quantum bit error rate (QBER) and the maximum secure transmission distance are analyzed. Taking the optical attenuation of ocean water into account, the performance bounds of QKD in different types of ocean water are discussed. The simulation results show that the maximum secure transmission distance of QKD gradually reduces as the incident angle from air to ocean water increases. In the clearest ocean water with the lowest attenuation, the maximum secure transmission distance of photons far exceeds the the working depth of underwater vehicles. In intermediate and murky ocean waters with higher attenuation, the secure transmission distance shortens, but the underwater vehicle can deploy other accessorial methods for QKD with perfect security. So the implementation of OKD between the satellite and the underwater vehicle is feasible.

Analysis on quantum bit error rate in measurement-device-independent quantum key distribution using weak coherent states

A measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to all detection side-channel attacks and guarantees the information-theoretical security even with uncharacterized single photon detectors. A weak coherent source is used in the current MDI-QKD experiments, it inevitably contains a certain percentage of vacuum and multi-photon pulses. The security issues introduced by these source imperfections can be avoided by applying the decoy state method. Here, through modeling experimental devices, and taking into account the weak coherent source and the threshold detectors, we have evaluated the gain, the probability to get successful Bell measurement and incorrect Bell measurement, and the quantum bit error rate (QBER), given a practical setup. In our simulation, we show how QBER varies with different transmission distances in the cases when the average photon numbers per pulse from Alice and Bob are symmetric and asymmetric. Result shows that the multi-photon pulses do not cause error in the Z basis of polarization encoding scheme, but produce a large QBER in phase encoding scheme and in the X basis of polarization encoding scheme. QBER is affected by the dark count rate and the system optical error associated with the multi-photon pulses. For different encoding schemes, QBER caused by each kind of average photon numbers from Alice and Bob increases to different degrees with the transmission distance, and finally is close to 50%. With the increase of the transmission distance, the average photon number per pulse decreases and the fraction of the dark count rate causing QBER gradually increases. Under the same effect of the dark count rate, the smaller the average photon number per pulse, the bigger the QBER. After a certain transmission and at the same transmission distance, the QBER is largest when average photon numbers used by Alice and Bob are both smallest. For the short distance transmission of phase encoding scheme and the X basis, we find that QBER is larger when average photon numbers from the two arms are asymmetric, as compared to the symmetric case. For the Z basis, the QBER caused by the system optical error and the dark count rate is very small.

Effect of electromagnetic disturbance on the practical QKD system in the smart grid

To improve the security of the smart grid, quantum key distribution (QKD) is an excellent choice. The rapid fluctuations on the power aerial optical cable and electromagnetic disturbance in substations are two main challenges for implementation of QKD. Due to insensitivity to birefringence of the channel, the stable phase-coding Faraday—Michelson QKD system is very practical in the smart grid. However, the electromagnetic disturbance in substations on this practical QKD system should be considered. The disturbance might change the rotation angle of the Faraday mirror, and would introduce an additional quantum bit error rate (QBER). We derive the new fringe visibility of the system and the additional QBER from the electromagnetic disturbance. In the worst case, the average additional QBER only increases about 0.17% due to the disturbance, which is relatively small to normal QBER values. We also find the way to degrade the electromagnetic disturbance on the QKD system.