Hosseiny Seyed Mohammad, Seyed-Yazdi Jamileh, Norouzi Milad
Physics Department, Faculty of Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Sci Rep. 2024 Aug 6;14(1):18261. doi: 10.1038/s41598-024-69081-4.
Non-Markovian effects due to quantum memory in the dynamics of open systems typically correspond to information backflows from the surrounding environment to the system. We propose a witness to quantify the non-Markovianity of quantum evolutions using the Bhattacharyya distance (BD), a specific quantum statistical distance. This witness has the advantage of not requiring the calculation of the evolved density matrix and only computes through the initial and final states of the system, therefore leading to the improvement of quantum metrology. It means that we calculate the quantum angle between two states to detect non-Markovian effects. This proposal is investigated by considering several instances of open quantum systems, such as two and three-level atoms interacting in single and two-mode fields, respectively, and two effective two-level atoms interacting locally with two independent environments. We demonstrate that the suggested BD-based non-Markovianity witness identifies memory effects, consistent with well-established witnesses based on Bures distance, quantum Fisher information, and Hilbert-Schmidt speed, showing sensitivity to information backflows.
开放系统动力学中量子记忆引起的非马尔可夫效应通常对应于信息从周围环境回流到系统。我们提出了一种使用特定量子统计距离——巴氏距离（BD）来量化量子演化非马尔可夫性的判据。该判据的优点是不需要计算演化后的密度矩阵，仅通过系统的初始态和末态进行计算，从而改进了量子计量学。这意味着我们通过计算两个态之间的量子角度来检测非马尔可夫效应。通过考虑几个开放量子系统的实例对该提议进行了研究，例如分别在单模和双模场中相互作用的两能级和三能级原子，以及与两个独立环境局部相互作用的两个有效两能级原子。我们证明，所建议的基于BD的非马尔可夫性判据能够识别记忆效应，与基于布雷尔斯距离、量子费希尔信息和希尔伯特 - 施密特速度的成熟判据一致，对信息回流表现出敏感性。
