Latency-Constrained Encoded Quantum Teleportation with Punctured Codes
Quantum teleportation is a key protocol for transmitting quantum information using entanglement and classical communication. Its reliability is constrained by both the availability and fidelity of shared entangled pairs, which are affected by stochastic generation and memory decoherence. In this work, we focus on encoded teleportation, in which quantum information is encoded using a quantum error-correcting code and transmitted as a codeword. We evaluate reliability in terms of logical error probability, considering latency-constrained settings where entanglement is accumulated over time and degrades while in memory. We develop a unified framework that captures the interaction between entanglement availability, decoherence, and coding decisions. Our results show that the benefits of longer codes depend on the availability and fidelity of entangled pairs, as acquiring additional resources introduces delays that can reduce their quality. To address this latency-reliability tradeoff, we leverage code puncturing to enable flexible encoded teleportation, allowing the effective code length to adapt across different latency regimes while preserving a common stabilizer structure. Numerical results show that encoded teleportation can provide substantial reliability gains over uncoded transmission under a common entanglement-acquisition latency constraint, and that selecting appropriate punctured codes improves performance across varying latency budgets. Overall, our results highlight the importance of resource-aware adaptation for reliable quantum networking.