The BB84 QKD protocol is based on the idea that the sender and the receiver can reconcile a certain fraction of the teleported qubits to detect eavesdropping or noise and decode the rest to use as a private key. Under the present hardware infrastructure, decoherence of quantum states poses a significant challenge to performing perfect or efficient teleportation, meaning that a teleportation-based protocol must be run multiple times to observe success. Thus, performance analyses of such protocols usually consider the completion time, i.e., the time until success, rather than the duration of a single attempt. Moreover, due to decoherence, the success of an attempt is in general dependent on the duration of individual phases of that attempt, as quantum states must wait in memory while the success or failure of a generation phase is communicated to the relevant parties. In this work, we do a performance analysis of the completion time of the BB84 protocol in a setting where the sender and the receiver are connected via a single quantum repeater and the only quantum channel between them does not see any adversarial attack. Assuming certain distributional forms for the generation and communication phases of teleportation, we provide a method to compute the MGF of the completion time and subsequently derive an estimate of the CDF and a bound on the tail probability. This result helps us gauge the (tail) behaviour of the completion time in terms of the parameters characterising the elementary phases of teleportation, without having to run the protocol multiple times. We also provide an efficient simulation scheme to generate the completion time, which relies on expressing the completion time in terms of aggregated teleportation times. We numerically compare our approach with a full-scale simulation and observe good agreement between them.
翻译:BB84 QKD协议的基本思想是发送方和接收方可以协调一定比例的传输比特以检测窃听或噪声,并将其解码以用作私钥。在当前硬件基础设施下,量子态的失相对于执行完美或高效的传送构成了重大挑战,这意味着必须多次运行基于传送的协议才能观察到成功。因此,这类协议的性能分析通常考虑完成时间,即直至成功所需的时间,而不是单个尝试的持续时间。此外,由于失相的影响,尝试的成功在一般情况下取决于该尝试的各个阶段的持续时间,因为在遗传阶段的成功或失败被传达给有关方之前,量子态必须在存储器中等待。在本文中,我们在一个发送方和接收方通过单个量子中继器相连且两者之间的唯一量子通道没有遭受对抗攻击的环境中对BB84协议完成时间进行性能分析。假设遗传和通信阶段的传输遵循一定的分布形式,我们提供了一种计算完成时间的MFG的方法,进而推断出CDF的估计和尾部概率的界限。这一结果帮助我们评估完成时间的(尾)行为,该时间以传送的基本阶段的参数为特征,而无需运行多次协议。我们还提供了一种有效的模拟方案来生成完成时间,该方案依赖于以聚合后的传送时间表达完成时间。我们通过与完整规模模拟进行数值比较,并观察它们之间良好的一致性。