光场环境中基于量子Fisher信息的参数估计

发布时间：2018-05-19 14:09

本文选题：量子Fisher信息 + 开放系统　；参考：《苏州科技大学》2017年硕士论文

【摘要】：本文主要以Boson光场环境中两能级系统为研究对象,重点讨论了不同类型的结构化光场环境和系统纠缠对量子退相干过程中相位参数估计精度的影响,从而为开放系统中的量子精密测量提供理论基础。本文的研究工作主要包括以下三个方面:首先,我们导出两能级系统的量子Fisher信息的几何表示,它表达式适用于任意混合态。我们发现Bloch矢量导数的模平方可以表示相位参数估计的量子Fisher信息,从几何角度上定量描述参数估计精度。利用这一结论,我们进一步研究了JaynesCummings原子-光场模型,利用含时量子主方程分析了量子Fisher信息的动力学演化。对于退振幅阻尼情形,我们发现Lorentzian频谱光场环境的频率失谐量会对量子Fisher信息的衰减产生影响。当系统与环境之间存在强耦合时,失谐量会明显抑制量子Fisher信息的衰减。在弱耦合条件下,虽然失谐也会减缓量子Fisher信息的衰减速率,但是这种抑制效果并不显著。对于退相位阻尼情形,我们发现Ohmic-like频谱环境的类欧姆系数s会对量子Fisher信息产生影响。当环境是次欧姆谱(s1)时,如果s越大,那么量子Fisher信息衰减越慢,而且总是单调减少的。对于超欧姆谱环境(s1),量子Fisher信息的数值会出现振荡现象。然后,本文考虑了多个纠缠的开放原子系统,每个原子与各自的独立光场环境存在相互作用。在驱动场的影响下,我们讨论了量子参数估计精度的动力学演化。我们用超算符映射方式得到了纠缠态的量子Fisher信息动力学。在一些特征时间内,纠缠态的参数估计精度要优于标准量子极限。在给定时间内,如果我们采用最优化的纠缠原子数目,参数估计精度可以提升至最大值。但是,纠缠原子的数目反而会加速量子Fisher信息的衰减。当原子与玻色场的耦合形式是类欧姆频谱函数时,如果增大频谱的幂指数s,那么我们可以在一定程度上抑制量子纠缠态的Fisher信息量的衰减。当频谱环境为洛伦兹谱时,我们发现耦合强度和失谐量也会对量子Fisher信息产生影响。最后,本文给出了广义局域测量对噪声通道中参数估计精度的影响。我们发现:在退相位通道中,广义局域测量可以抵消初态极化角参数的影响;在退振幅通道中,它可以完全消除环境参数的影响;在退极化通道中,局域测量也可以部分消除极化角参数的影响。总之,利用广义局域测量可以保护噪声通道中参数估计精度。
[Abstract]:In this paper, the two-level system in Boson light field is studied, and the effect of different structured light field environment and system entanglement on the precision of phase parameter estimation in the process of quantum decoherence is discussed. It provides a theoretical basis for quantum precision measurement in open system. The work of this paper mainly includes the following three aspects: first, we derive the geometric representation of quantum Fisher information for two-level systems, which is suitable for arbitrary mixed states. We find that the modulus square of the Bloch vector derivative can represent the quantum Fisher information of the phase parameter estimation, and quantitatively describe the precision of the parameter estimation from the geometric point of view. Using this conclusion, we further study the atom-light field model of JaynesCummings, and analyze the dynamical evolution of quantum Fisher information by time-dependent quantum master equation. In the case of dedamped amplitude, we find that the frequency detuning in the environment of Lorentzian spectrum light field has an effect on the attenuation of quantum Fisher information. When there is a strong coupling between the system and the environment, the detuning will obviously suppress the attenuation of the quantum Fisher information. Under weak coupling conditions, detuning can also slow down the attenuation rate of quantum Fisher information, but the effect is not significant. For the dephase damping case, we find that the ohmm-like coefficient s of the Ohmic-like spectrum environment has an effect on the quantum Fisher information. When the environment is a sub-ohmic spectrum s1), if s is larger, the quantum Fisher information will decay more slowly and monotonously. For the superohmic environment, the quantum Fisher information oscillates numerically. Then we consider several entangled open atomic systems in which each atom interacts with its own independent light field environment. Under the influence of the driving field, we discuss the dynamic evolution of the estimation accuracy of quantum parameters. We obtain the quantum Fisher information dynamics of entangled states by means of hyper-operator mapping. In some characteristic time, the parameter estimation accuracy of entangled state is better than the standard quantum limit. If we use the optimal number of entangled atoms in a given time, the precision of parameter estimation can be increased to the maximum. However, the number of entangled atoms will accelerate the decay of quantum Fisher information. When the coupling form of atom and boson field is ohmm-like spectrum function, if we increase the power exponent s of the spectrum, we can restrain the attenuation of the Fisher information of the quantum entangled state to some extent. When the spectrum environment is Lorentz spectrum, we find that the coupling intensity and detuning also affect the quantum Fisher information. Finally, the effect of generalized local measurement on the accuracy of parameter estimation in noise channels is given. We find that in the dephase channel, the generalized local measurement can counteract the influence of the initial state polarization angle parameter, in the depolarization amplitude channel, it can completely eliminate the influence of the environmental parameter; in the depolarization channel, the influence of the environmental parameters can be completely eliminated. Local measurement can also partially eliminate the influence of polarization angle parameters. In a word, the accuracy of parameter estimation in noise channels can be protected by generalized local measurement.
【学位授予单位】：苏州科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O413

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