The characteristics of quantum channel play important roles on designing a high performance quantum communication system. In this paper, we analyze the fidelity of polarization state travelling through a non-Markovian optical fiber depolarizing quantum channel with color noise environment. The quantum bit error rate (QBER) of a polarization coding BB84 quantum key distribution (QKD) system under non-Markovian depolarizing channel is also discussed. Analysis results show that there are several security regions caused by the fluctuation of QBER in such a non-Markovian channel. These will provide references for designing polarization compensation scheme and estimating of secure distance.
The characteristics of quantum channel play important roles on designing a high performance quantum communication system. In this paper, we analyze the fidelity of polarization state travelling through a non-Markovian optical fiber depolarizing quantum channel with color noise environment. The quantum bit error rate (QBER) of a polarization coding BB84 quantum key distribution (QKD) system under non-Markovian depolarizing channel is also discussed. Analysis results show that there are several security regions caused by the fluctuation of QBER in such a non-Markovian channel. These will provide references for designing polarization compensation scheme and estimating of secure distance.
The dynamic of the secret key rate of the discrete-variable quantum key distribution (QKD) protocol over the non-Markovian quantum channel is investigated. In particular, we calculate the secret key rate for the six-state protocol over non-Markovian depolarizing channels with coloured noise and Markovian depolarizing channels with Gaussian white noise, respectively. We find that the secure secret key rate for the non-Markovian depolarizing channel will be larger than the Markovian one under the same conditions even when their upper bounds of tolerable quantum bit error rate are equal. This indicates that this coloured noise in the non-Markovian depolarizing channel can enhance the security of communication. Moreover, we show that the secret key rate fluctuates near the secure point when the coupling strength of the system with the environment is high. The results demonstrate that the non-Markovian effects of the transmission channel can have a positive impact on the security of discrete-variable QKD.
Underwater quantum key distribution (QKD) has potential applications in absolutely secure underwater communication. However, the performance of underwater QKD is limited by the optical elements, background light, and dark counts of the detector. In this paper, we propose a modified formula for the quantum bit error rate (QBER), which takes into account the effect of detector efficiency on the QBER caused by the background light. Then we calculate the QBER of the polarization encoding BB84 protocol in Jerlov-type seawater by analyzing the effect of the background light and optical components in a more realistic situation. Finally, we further analyze the final key rate and the maximum secure communication distance in three propagation modes, i.e., upward, downward, and horizontal modes. We find that secure QKD can be performed in the clearest Jerlov-type seawater at a distance of hundreds of meters, even in the worst downward propagation mode. Specifically, by optimizing the system parameters, it is possible to securely transmit information with a rate of 67 kbits/s at a distance of 100 m in the seawater channel with an attenuation coefficient of 0.03/m at night. For practical underwater QKD, the performance can also be improved by using decoy states. Our results are useful for long-distance underwater quantum communication.
Quantum Key Distribution (QKD) provides information-theoretic security by exploiting the principles of quantum mechanics. Among QKD protocols, the BB84 scheme remains the most widely adopted for both theoretical research and practical implementation. A critical parameter determining the reliability and security of BB84 is the Quantum Bit Error Rate (QBER), which quantifies errors in the sifted key arising from channel noise or potential eavesdropping. This paper presents a systematic review and analysis of QBER within the BB84 protocol, examining its calculation, statistical estimation methods, and role in detecting eavesdropping activity. Simulation results, corroborated by reported experimental observations, reveal a near-linear relationship between eavesdropping intensity and QBER, with values approaching 25% under full intercept-resend attacks. Four confidence interval estimation methods, Wald, Wilson, Clopper-Pearson, and Hoeffding's inequality, are compared for robust QBER analysis in finite-key scenarios. Protocol enhancements, including decoy-state methods, hybrid cryptographic models, and quantum-resistant authentication, are discussed as mechanisms to mitigate errors and strengthen resilience across fiber, free-space, underwater, and satellite QKD systems. Open challenges in distinguishing noise-induced errors from malicious eavesdropping, and the role of adaptive error correction and machine-learning-assisted QBER estimation in future quantum networks, are identified as key directions for further research.
A quantum key distribution system based on the subcarrier wave modulation method has been demonstrated which employs the BB84 protocol with a strong reference to generate secure bits at a rate of 16.5 kbit/s with an error of 0.5% over an optical channel of 10 dB loss, and 18 bits/s with an error of 0.75% over 25 dB of channel loss. To the best of our knowledge, these results represent the highest channel loss reported for secure quantum key distribution using the subcarrier wave approach. A passive unidirectional scheme has been used to compensate for the polarization dependence of the phase modulators in the receiver module, which resulted in a high visibility of 98.8%. The system is thus fully insensitive to polarization fluctuations and robust to environmental changes, making the approach promising for use in optical telecommunication networks. Further improvements in secure key rate and transmission distance can be achieved by implementing the decoy states protocol or by optimizing the mean photon number used in line with experimental parameters.
The hybrid modulation quantum key distribution(QKD) via single-photon two-qubit states scheme is analyzed,and an improvement scheme is proposed.The input-output model of polarization is established.And the influence of the interferometers on the polarization coding is analyzed.Quantum bit error rate(QBER) of polarization coding caused by the phasic error of fast and slow axes and the alignment error between the basis vectors of polarization and polarization axis is simulated.Furthermore,the stability conditions of polarization are derived on this basis.The QBER of polarization coding can be influenced deeply by the fiber M-Z interferometers.The theoretic analysis reveals that the jitter of polarization state is not only derived from the birefringency,but also derived from coordinate system difference between incident light and fast and slow axes in fiber interferometer.Some necessary conditoins for the QKD via single-photon two-qubit states are given.The simulation show that when ρ and θ are both below 0.2 rad,the polarization QBER is less than 0.015.When ρ and θ are both below 0.4 rad,the polarization QBER is less than 0.06.The polarization QBER of 2%-5% in two-qubit QKD scheme could be accepted as far as the safety upper limit of QBER(11%) is concerned.
This study compares the quantum bit error rate (QBER) performance of BB84, SARG04, and the entanglement-based BBM92 protocol in non-turbulent underwater optical channels. Clear, coastal, and turbid water types are considered under different background-illumination and receiver configurations. For BB84 and SARG04, channel attenuation and background-induced detections determine the quantum gain and QBER. For BBM92, photon loss is included through the two arm detection efficiencies, whereas the polarization state conditioned on two-photon detection is described by local depolarizing Kraus channels. The BBM92 QBER is obtained from the correlations in both measurement bases and from an exact partition of recorded events into true and false coincidences. Stochastic numerical estimates provide consistency checks of the analytical implementation. The results show that water turbidity and optical background reduce the distance below the adopted QBER threshold. They also show that a low conditional BBM92 QBER may coexist with a very small coincidence probability; therefore, the QBER-threshold distance alone does not represent a complete operational or secret-key-rate bound.