Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 10 1 2025 03 01 A review on perfect, pretty good, state transfers and their applications 87 142 2190 10.22061/jdma.2024.11198.1091 EN Afsaneh Khalilipour Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, I. R. Iran Modjtaba Ghorbani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, I. R. Iran Majid Arezoomand Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, I. R. Iran Journal Article 2024 08 23 In this study, we review two significant topics: perfect State Transfer (PST) and Pretty Good State Transfer (PGST). These concepts involve designing interactions within a chain of spins on graph structures of networks, enabling a quantum state initially placed at one end to be perfectly or pretty transferred to the opposite end within a specified timeframe. PST and PGST play crucial roles in applications such as quantum information processing, quantum communication networks, and quantum chemistry. perfect state transfer Pretty good state transfer Cayley graph https://jdma.sru.ac.ir/article_2190_3f9aa20ea4a2bb064bf9e758dafade24.pdf