量子速度极限研究进展

Advances on quantum speed limit

研究量子速度极限不仅有助于理解量子力学基本问题,而且在量子模拟、量子非平衡热力学等领域亦有重要意义.本文首先介绍了封闭系统中两个重要的量子速度极限——Mandelstam-Tamm界和Margolus-Levitin界以及封闭系统的量子速度极限统一界.在开放量子系统中,由于系统与环境相互作用,量子系统一般不能实现正交态演化,研究开放系统量子速度极限需要考虑初态与末态之间测地线的度量方式.本文讨论了基于不同几何度量所建立的量子速度极限以及开放系统的量子速度极限统一界.基于量子力学的规范不变特性,我们建立了一个新的量子速度极限界,将量子系统演化速度与几何相位关联起来,说明量子速度极限对量子热力学、几何操控量子系统动力学演化具有重要意义.此外,基于半经典Wigner函数表示,我们也建立了量子速度极限界.最后,本文回顾了外部环境与量子系统动力学过程对量子系统演化速度极限的重要影响,并对量子速度极限的下一步研究作出展望.

As one of the fundamental questions,quantum speed limit(QSL)is of vital role in the community of quantum physics,which sets the ultimate,maximal speed with which a quantum system can evolve.QSL originated from the understanding of the Heisenberg uncertainty relation.In 1945,Mandelstam and Tamm found the timeΔt in the celebrated relationΔEΔt≥?could be thought as the minimum time that a quantum system needs to evolve from an initial state to the orthogonal state for unitary evolution.QSL sets the lower bound of the evolution.They established the relationship between the minimum evolution time(τQSL)and the energy uncertainty of the system(ΔE),namelyτQSL=π?/(2ΔE),the Mandelstam-Tamm(MT)bound.Later,Margolus and Levitin derived another different bound for a closed system which connected theτQSL with the average energy of the system(),i.e.,τQSL=π?/(2),the Margolus-Levitin(ML)bound.Combining the MT and ML bounds together,we can have a unified bound for a unitary system and orthogonal states.In the case of open system dynamics,because there is energy and/or coherence exchange between the system and the environment,the orthogonal final state of the initial state can hardly be reached any longer.An investigation of the QSL on non-unitary quantum evolution needs to be considered.The generalized QSLs are established by employing the distance between the distinguishable states.Different metrics define different distances,leading to different QSL bounds.We show a few typical generalized QSL bounds based on different metrics.And the unified QSL bound for non-unitary evolution is obtained by combining the generalized MT and ML bounds under the same metric.The generations and developments of QSL have successfully generalized the MT bounds.Even the ML bounds have been attempted to generalize,the current studies of ML bound are thought as the significantly harder task,and keep as the open questions.The influences of external environment and quantum system dynamics which include the role of entanglement in QSL for open dynamics and many-body systems,the relation between the maximum interaction speed and QSL in quantum spin systems,the non-Markovianity effect of the environment on accelerating the speed of evolution have been investigated.Furthermore,by employing the gauge invariant distance in the Riemannian metric,we establish a distinct QSL bound,which relates the quantum speed limit time to the geometry phase,and presents the geometric and gauge invariant properties of it.The bound shows the impacts of the transmission modes of the state vectors on the evolution path in the manifold.Different from the established MT and ML bounds,our bound establishes the relation between the QSL and the Pancharatnam connection 1-form,and our results show that the QSL can be controlled via manipulating the generalized Pahcharatnam connection.Also,our results of QSL are holonomy via the generalized Pahcharatnam connection,which show us a possible technique to speed up the holonomic quantum computation.The bound is also interesting to the metrology and non-equilibrium thermodynamics,etc.QSL has also been studied in the quantum representation of Wigner function.In the future research of quantum speed limit,there are many issues that need to be considered,such as the generalized ML bound,the unified QSL bound under different metrics,the application of maximum rate of quantum information derived from the QSL,and the relation between the quantum speed limit and the quantum heat engine,etc.