Single-photon addition and subtraction are fundamental operations in quantum information processing. Traditionally, the behavior of a single-photon adder (SPA) and single-photon subtractor (SPS) has been theoretically described using creation and annihilation operators, respectively. However, we demonstrate that this ladder-operator-based description contains significant theoretical flaws. To address these issues, we develop a theoretical framework based on Kraus operators, applicable to both coherent and incoherent SPAs and SPSs. Furthermore, we propose a method for realizing deterministic SPAs and SPSs of a cavity mode using three-level atoms. We analyze the effects of these operations on various quantum states. Additionally, we demonstrate that the use of a control pulse could enhance the performance of SPAs and SPSs, effectively preserving the quantum coherence of the resulting photon state.
Cite
@article{arxiv.2502.11376,
title = {Deterministic Single-Photon Adder and Subtractor},
author = {Si-Qi Jiang and Hai-Jun Xing and Li-Ping Yang},
journal= {arXiv preprint arXiv:2502.11376},
year = {2025}
}