Quantum teleportation is a foundational protocol for sending quantum information through entanglement distribution and classical communication. Assuming ideal classical communication, the reliability of quantum teleportation is limited by the fidelity of the shared EPR pairs. This reliability can be improved through two mechanisms: entanglement purification and quantum error correction (QEC). Using both techniques in concert requires flexible QEC rates, since purification alters the structure of errors induced by imperfect-EPR teleportation, and fixed-rate codes cannot be uniformly effective across purification regimes or reliability targets. In this work, we supplement purification with punctured QEC codes, providing a family of code variants that can be adapted to error-channel characteristics and reliability targets. Punctured codes improve teleportation reliability across a broader range of purification regimes, enabling target reliability to be met without hardware-level code switching. This is corroborated by numerical results, showing that different punctured codes achieve the lowest logical error probability in different operating regimes, and that selecting among them reduces logical error relative to fixed-rate encoded teleportation. This reduction relaxes the requirement on the initial EPR fidelity or purification needed to achieve a target reliability. Overall, puncturing enables adaptation to varying entanglement conditions and reliability requirements while reusing a single stabilizer structure.

翻译：量子隐形传态是通过纠缠分发与经典通信传输量子信息的基础协议。在假设经典通信理想的情况下，量子隐形传态的可靠性受限于共享EPR对保真度。可通过两种机制提升可靠性：纠缠纯化与量子纠错码。协同使用这两种技术需要灵活的QEC码率，因为纯化会改变非完美EPR隐形传态所诱发错误的结构，而固定码率的编码无法在纯化区间或可靠性目标间保持均匀有效性。本工作通过穿孔QEC码增强纯化过程，提供一系列可适配错误信道特性与可靠性目标的码型变体。穿孔码能在更广泛的纯化区间内提升隐形传态可靠性，无需硬件层面的编码切换即可达成目标可靠性。数值结果证实：不同穿孔码在不同工作区间实现最低逻辑错误概率，且通过码型选择可降低相对于固定码率编码隐形传态的逻辑错误。这种降低放宽了实现目标可靠性所需的初始EPR保真度或纯化要求。总体而言，穿孔技术能在复用单一稳定子结构的同时，适配变化的纠缠条件与可靠性需求。