2017/10/31 by E. Shchukin, F. Schmidt, Frank L. Schmidt +2
Computer Science · Physics and Astronomy · #Artificial intelligence #Computer science #Physics #Probabilistic logic #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #quant-ph
paper · pdf · doi:10.1103/physreva.100.032322
published as Phys. Rev. A 100, 032322 (2019) · 23 pages, 12 figures
arxiv created 2019/09/16 · openalex publication_date 2019/09/16 · arxiv updated 2019/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters, calculating repeater rates has typically depended on approximations assuming sufficiently small probabilities. Here we propose an exact and systematic approach including an algorithm based on Markov chain theory to compute the average waiting time (and hence the transmission rates) of quantum repeaters with arbitrary numbers of links. For up to four repeater segments, we explicitly give the exact rate formulas for arbitrary entanglement swapping probabilities. Starting with three segments, we explore schemes with arbitrary (not only doubling) and dynamical (not only predetermined) connections. The effect of finite memory times is also considered and the relative influence of the classical communication (of heralded signals) is shown to grow significantly for larger probabilities. Conversely, we demonstrate that for small swapping probabilities the statistical behavior of the waiting time in a quantum repeater cannot be characterized by its average value alone and additional statistical quantifiers are needed. For large repeater systems, we propose a recursive approach based on exactly but still efficiently computable waiting times of sufficiently small subrepeaters. This approach leads to better lower bounds on repeater rates compared to existing schemes.