Practical decoy-state BB84 quantum key distribution with quantum memory

We generalize BB84 quantum key distribution(QKD) to the scenario where the receiver adopts a heralded quantum memory(QM). With the heralded QM, the valid dark count rate of the receiver's single photon detectors can be mitigated obviously, which will lower the quantum bit error rate, and thus improve the performance of decoy-state BB84 QKD systems in long distance range. Simulation results show that, with practical experimental system parameters, decoy-state BB84 QKD with QM can exhibit performance comparable to that of without QM in short distance range, and exhibit performance better than that without QM in long distance range.     

Quantum key distribution with two-qubit quantum codes

We propose a prepare-and-measure scheme for quantum key distribution with two-qubit quantum codes. The protocol is unconditionally secure under all types of intercept-and-resend attack. Given the symmetric and independent errors to the transmitted qubits, our scheme can tolerate a bit of an error rate up to 26% in four-state protocol and 30% in six-state protocol, respectively. These values are higher than all currently known threshold values for the prepare-and-measure protocols. Moreover, we give a practically implementable linear optics realization for our scheme.     

Implementation of polarization-coded free-space BB84 quantum key distribution

We report on the implementation of a Bennett-Brassard 1984 quantum key distribution protocol over a free-space optical path on an optical table. Attenuated laser pulses and Pockels cells driven by a pseudorandom number generator are employed to prepare polarization-encoded photons. The sifted key generation rate of 23.6 kbits per second and the quantum bit error rate (QBER) of 3% have been demonstrated at the average photon number per pulse μ = 0.16. This QBER is sufficiently low to extract final secret keys from shared sifted keys via error correction and privacy amplification. We also tested the long-distance capability of our system by adding optical losses to the quantum channel and found that the QBER remains the same regardless of the loss.     

Error corrections of quantum key distribution of the quantum codes via optical wireless link

Quantum key generated by using a fiber optic Mach Zehnder interferometer incorporating a fiber optic ring resonator is proposed. The generated quantum key is distributed via an optical wireless link system, which is available for the free space link. The random quantum bits can be formed and used as the secret codes in quantum communication system. By adding an ancillary photon after the signal photon within the correlation time of the fiber noise and by performing quantum parity checking, the high fidelity to the noiseless quantum in free space is achieved by the technique known as the quantum error correction.     

Simple proof of security of the BB84 quantum key distribution protocol

We prove that the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution is secure. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement purification based protocol uses Calderbank-Shor-Steane codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.     

High efficiency continuous-variable quantum key distribution based on QC-LDPC codes

Seeking good error correcting codes to improve the efficiency of continuous-variable quantum key distribution(CVQKD) reconciliation is a concerning issue. Due to the introduction of multidimensional reconciliation, the error correcting techniques in the classical binary-input additive white Gaussian noise channel are applicable to CVQKD. In this Letter, we apply the quasi-cyclic low-density parity-check(QC-LDPC) codes, which are specified in 5 G protocol, to the reconciliation process. Simulation results show that the reconciliation efficiency can reach 92.6% when the code rate is 22/68 and the signal-to-noise ratio is 0.623. Such a new error correcting code points out a new direction for the development of CVQKD.     

Security of biased BB84 quantum key distribution with finite resource

In the original BB84 quantum key distribution protocol, the states are prepared and measured randomly, which lose the unmatched detection results. To improve the sifting efficiency, biased bases selection BB84 protocol is proposed. Meanwhile, a practical quantum key distribution protocol can only transmit a finite number of signals, resulting in keys of finite length. The previous techniques for finite-key analysis focus mainly on the statistical fluctuations of the error rates and yields of the qubits. However, the prior choice probabilities of the two bases also have fluctuations by taking into account the finite-size effect. In this paper, we discuss the security of biased decoy state BB84 protocol with finite resources by considering all of the statistical fluctuations. The results can be directly used in the experimental realizations.     

On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

Some MIT researchers [Phys. Rev. A 75, 042327 (2007)] have recently claimed that their implementation of the Slutsky-Brandt attack [Phys. Rev. A 57, 2383 (1998); Phys. Rev. A 71, 042312 (2005)] to the BB84 quantum-key-distribution (QKD) protocol puts the security of this protocol “to the test” by simulating “the most powerful individual-photon attack” [Phys. Rev. A 73, 012315 (2006)]. A related unfortunate news feature by a scientific journal [G. Brumfiel, Quantum cryptography is hacked, News @ Nature (april 2007); Nature 447, 372 (2007)] has spurred some concern in the QKD community and among the general public by misinterpreting the implications of this work. The present article proves the existence of a stronger individual attack on QKD protocols with encrypted error correction, for which tight bounds are shown, and clarifies why the claims of the news feature incorrectly suggest a contradiction with the established “old-style” theory of BB84 individual attacks. The full implementation of a quantum cryptographic protocol includes a reconciliation and a privacy-amplification stage, whose choice alters in general both the maximum extractable secret and the optimal eavesdropping attack. The authors of [Phys. Rev. A 75, 042327 (2007)] are concerned only with the error-free part of the so-called sifted string, and do not consider faulty bits, which, in the version of their protocol, are discarded. When using the provably superior reconciliation approach of encrypted error correction (instead of error discard), the Slutsky-Brandt attack is no more optimal and does not “threaten” the security bound derived by Lütkenhaus [Phys. Rev. A 59, 3301 (1999)]. It is shown that the method of Slutsky and collaborators [Phys. Rev. A 57, 2383 (1998)] can be adapted to reconciliation with error correction, and that the optimal entangling probe can be explicitly found. Moreover, this attack fills Lütkenhaus bound, proving that it is tight (a fact which was not previously known).     

Cryptographic robustness of practical quantum cryptography: BB84 key distribution protocol

In real fiber-optic quantum cryptography systems, the avalanche photodiodes are not perfect, the source of quantum states is not a single-photon one, and the communication channel is lossy. For these reasons, key distribution is impossible under certain conditions for the system parameters. A simple analysis is performed to find relations between the parameters of real cryptography systems and the length of the quantum channel that guarantee secure quantum key distribution when the eavesdropper’s capabilities are limited only by fundamental laws of quantum mechanics while the devices employed by the legitimate users are based on current technologies. Critical values are determined for the rate of secure real-time key generation that can be reached under the current technology level. Calculations show that the upper bound on channel length can be as high as 300 km for imperfect photodetectors (avalanche photodiodes) with present-day quantum efficiency (η ≈ 20%) and dark count probability (p _dark ～ 10^?7).     

Upper bound on key generation rate of quantum key distribution with two-way or two-step quantum channels

We present an asymptotic security proof of deterministic quantum key distribution (DQKD) with a two-way quantum channel. The security proof of DQKD with a two-way quantum channel is different from that of BB84, because Eve can attack the travel qubits twice, both in line Bob to Alice and in line Alice to Bob. With the no-signaling principle and the property of mutual information, we obtain an upper bound of the final key generation of entanglement-based DQKD and hence single-photon four-state DQKD. Our results can be applied to the protocol of QKD with two-step quantum channels.     

Quantum scheme for an optimal attack on quantum key distribution protocol BB84

A quantum scheme for an optimal attack on protocol BB84, the most studied protocol of quantum cryptography, is constructed. The physical implementation of this scheme on the basis of linear fiber-optical elements and the two-particle “controlled NOT” quantum transformation is proposed.     

Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes

In the practical continuous-variable quantum key distribution(CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check(MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio(SNR).However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC(RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. Moreover, this technique can significantly reduce the cost of constructing a new matrix. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than-16.45 d B. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances.     

Shor and Preskill's and Mayers's security proof for the BB84 quantum key distribution protocol

We review two security proofs for the BB84 quantum key distribution protocol: Mayers's security proof and the more recent proof of Shor and Preskill. We focus on the basic principles and the intuition in Mayers's proof instead of technical details. We present a variation on Shor's and Preskill's proof which is convenient for purpose of comparison. We explain the connection between these two proofs. Received 14 July 2001     

用于BB84相位编码量子密钥分发系统的不间断式主动相位补偿方案

提出一种新的不间断的主动相位补偿方案,在进行量子密钥分发的同时统计不匹配基量子比特在干涉仪不同输出端口上的随机计数分布,给出了由不匹配基量子比特统计数值计算相位漂移参数的计算公式,并由统计数值计算得到相位漂移参数。结果表明：该方案允许系统并行处理量子密钥分发与相位补偿,也充分利用了在原BB84协议中会被丢弃的不匹配基量子比特信息。     

用于BB84相位编码量子密钥分发系统的不间断式主动相位补偿方案

提出一种新的不间断的主动相位补偿方案,在进行量子密钥分发的同时统计不匹配基量子比特在干涉仪不同输出端口上的随机计数分布,给出了由不匹配基量子比特统计数值计算相位漂移参数的计算公式,并由统计数值计算得到相位漂移参数.结果表明:该方案允许系统并行处理量子密钥分发与相位补偿,也充分利用了在原BB84协议中会被丢弃的不匹配基量...     

基于弱相干光源测量设备无关量子密钥分发系统的误码率分析

测量设备无关量子密钥分发系统可以免疫任何针对探测器边信道的攻击, 并进一步结合诱惑态方法规避了准单光子源引入的实际安全性问题. 目前实验中一般采用弱相干光源, 但是该光源含有一定比例的空脉冲和多光子脉冲. 本文针对弱相干光源的具体特性, 采用量子力学的描述, 将各个器件进行量子化处理, 并同时考虑探测器的具体性能参数的影响, 分别给出了通信双方各自发送的脉冲含有特定光子数时产生的成功贝尔态和错误贝尔态的概率公式, 从理论上对相位编码和偏振编码测量设备无关量子密钥分发系统的误码率进行了定量分析, 分别推导并模拟了通信双方采用的平均光子数对称和不对称时误码率随传输距离的变化情况, 结果表明在偏振编码Z基中, 多光子脉冲不会引起误码; 在偏振编码X基和相位编码中, 受多光子影响, 产生的误码率较大. 对于不同的编码方式, 误码率均随传输距离的增加有不同程度的升高, 长距离传输时, 平均光子数越小, 产生的误码率越大; 在偏振编码X基和相位编码的短距离传输中, 相对于对称, 通信双方采用的平均光子数不对称时产生的误码率较大.     

Encoding entanglement-assisted quantum stabilizer codes

We address the problem of encoding entanglement-assisted (EA) quantum error-correcting codes (QECCs) and of the corresponding complexity. We present an iterative algorithm from which a quantum circuit composed of CNOT, H, and S gates can be derived directly with complexity O(n²) to encode the qubits being sent. Moreover, we derive the number of each gate consumed in our algorithm according to which we can design EA QECCs with low encoding complexity. Another advantage brought by our algorithm is the easiness and efficiency of programming on classical computers.     

一种基于确定性量子密钥分发误码判据的相位调制器半波电压的精确测定方法

基于相位编码的量子密钥分发系统需要对信息加载的相位调制器的半波电压进行精确的测定以减小量子密钥的误码率,相位调制器半波电压的测量精度直接影响到了量子密钥分发系统的最终误码.本文提出了一种基于确定性量子密钥分发误码率判据的相位调制器半波电压的精确测定方法,所采用相位调制器的半波电压的测量精度达到了2mV,实验结果表明这种方法可以用于量子密钥分发实际应用系统中实时获得不同条件下的行波相位调制器的半波电压以最大程度地减小由于相位信息不准确加载而带来的系统误码.     

Nonperturbative gadget for topological quantum codes

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly nonlocal interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. In this Letter, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians nonperturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasiparticle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other nonlocal spin Hamiltonians may be possible.