近日，印度Harish-Chandra研究所的Ujjwal Sen&Vivek Pandey与美国德克萨斯理工大学的Brij Mohan等人合作并取得一项新进展。经过不懈努力，他们成功推导出二体量子系统纠缠动力学的基本速度极限。相关研究成果已于2024年11月14日在国际知名学术期刊《物理评论A》上发表。

纠缠的速度极限定义为在物理过程中，纠缠可以生成或降解的最大速率。该研究团队推导了纠缠的速度极限，分别采用了相对熵纠缠度和迹距离纠缠度，针对幺正量子动力学和任意量子动力学进行了推导。在此过程中，研究人员假设最接近可分离态的动力学，可以近似地由系统实际动力学中最接近的可分离动力学来描述。

对于由纯态描述的孤立二体系统的幺正动力学，纠缠产生的速率受到系统驱动哈密顿量和惊异算符（surprisal operator）波动的乘积的限制，并附加一个反映最接近可分离态时间依赖性的项。当去除对输入态纯度以及动力学幺正性的限制后，界限中的两项会相应地发生变化。

此外，研究人员还发现了通过任意量子动力学，生成或降解一定量纠缠所需时间的下限。通过考虑具有实际意义的量子过程，研究人员验证了纠缠速度极限的紧密性。

附：英文原文

Title: Fundamental speed limits on entanglement dynamics of bipartite quantum systems

Author: Vivek Pandey, Swapnil Bhowmick, Brij Mohan, Sohail, Ujjwal Sen

Issue&Volume: 2024/11/14

Abstract: The speed limit on entanglement is defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and trace-distance entanglement, for unitary and arbitrary quantum dynamics, where we assume that the dynamics of the closest separable state can be approximately described by the closest separable dynamics of the actual dynamics of the system. For the unitary dynamics of isolated bipartite systems which are described by pure states, the rate of entanglement production is bounded by the product of fluctuations of the system's driving Hamiltonian and the surprisal operator, with an additional term reflecting the time-dependent nature of the closest separable state. Removing restrictions on the purity of the input and on the unitarity of the evolution, the two terms in the bound get suitably altered. Furthermore, we find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics. We demonstrate the tightness of our speed limits on entanglement by considering quantum processes of practical interest.

DOI: 10.1103/PhysRevA.110.052420

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.052420