Measurement-Based Entanglement Distillation and Constant-Rate Quantum Repeaters over Arbitrary Distances

Abstract: Measurement-based quantum repeaters employ entanglement distillation and swapping across links using locally prepared resource states of minimal size and local Bell measurements. In this paper, we introduce a systematic protocol for measurement-based entanglement distillation and its application to repeaters that can leverage any stabilizer code. Given a code, we explicitly define the corresponding resource state and derive an error-recovery operation based on all Bell measurement outcomes. Our approach offers deeper insights into the impact of resource state noise on repeater performance while also providing strategies for efficient preparation and fault-tolerant preservation of resource states. As an application, we propose a measurement-based repeater protocol based on quantum low-density parity-check (QLDPC) codes, enabling constant-yield Bell state distribution over arbitrary distances. Numerical simulations confirm exponential suppression of infidelity with increasing code size while maintaining a fixed code rate. This work establishes a scalable backbone for future global-scale fault-tolerant quantum networks.