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摘要

最近, 基于量子信息理论的统计复杂度引起了人们的关注. 在噪声环境下, 一个受外界驱动的单量子比特系统具有丰富的动力学行为. 本文利用Lindblad方程, 在Born-Markov近似下, 研究 $N$ 次中间量子测量后, 在系统演化的最后时刻 $\tau$ , 末态的统计复杂度 $C$ . 研究发现: 在 $\tau$ 由0变大的过程中, $C$ 从0开始, 先增大到最大值, 然后减小, 直到再趋近于0; $N$ 较小时, $C$ 伴随着明显的不规则振荡现象, 振幅随 $\tau$ 逐渐减小; $N$ 越大, $C$ 随 $\tau$ 的变化趋势越接近无中间测量时的变化趋势. 研究结果给量子态的操控提供了一定的理论参考.

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Abstract

Recently, quantum statistical complexity based quantum information theory has received much attraction. Quantum measurements can extract the information from a system and may change its state. At the same time, the method of measuring multiple quantum is an important quantum control technique in quantum information science and condensed matter physics. The main goal of this work is to investigate the influence of multiple quantum measurements on quantum statistical complexity. It is a fundamental problem to understand, characterize, and measure the complexity of a system. To address the issue, a damped and linearly driven two-level system (qubit) is taken for example. The driving amplitude and dephasing intensity are considered. By using the Lindblad equation and the Born-Markov approximation, the time evolution of the system can be obtained. Under multiple intermediated measurements, the system has a complex dynamic behavior. Quantum statistical complexity $C$ at the last moment $\tau$ is studied in detail. The results show that on the whole, $C$ first increases from zero to a maximal value with $\tau$ increasing, then decreases, and finally it approaches to zero. At first, the system is in a pure state and $C=0$ . Finally, the system is in a maximally mixed state due to the interaction with the environment and $C=0$ again. When the number of measurements $N$ is relatively small, $C$ fluctuates with $\tau$ increasing, but when $N$ is relatively large, the fluctuations disappear. Due to the quantum Zeno effect, as $N$ is larger, the variation of $C$ with $\tau$ is similar to that for the case of no intermediated measurement. Because of the quantum superposition principle, uncertainty principle, and quantum collapse, quantum measurement can disturb the system, so quantum statistical complexity $C$ exhibits a complex behavior. In the quantum realm, the complexity of a system can be transformed into a resource. The quantum state needs creating, operating, or measuring. Therefore, all our results provide a theoretical reference for the optimal controlling of quantum information process and condensed matter physics. At the same time, the number of the degrees of freedom is two for the damped and linearly driven two-level system, so this system is simple and easy to study. The complexity of such a system can be tailored by properly tuning the driving strength. Therefore, the model can be used as a typical example to study the quantum statistical complexity.

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通信作者:巩龙延,lygong@njupt.edu.cn

基金项目:国家自然科学基金 (批准号: 61271238, 61475075)资助的课题.

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Corresponding author:Gong Long-Yan,lygong@njupt.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 61271238, 61475075)

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