光子晶体中的量子费舍信息和熵压缩

发布时间：2018-06-21 00:30

本文选题：量子费舍信息 + 熵压缩　；参考：《山西大学》2017年硕士论文

【摘要】：计量学是研究测量及测量误差的一门学科,而量子计量学是计量学与量子力学相互结合的产物,其主要任务是实现量子精密测量。由于测量精度与参数测量过程密切相关,因此测量精度的提高就意味着实验准确性的提高。从参数估计的基本理论——量子克拉美罗(Cramér-Rao)定理可知,测量的最低界限由量子费舍信息(quantum Fisher information,QFI)确定,这里的量子费舍信息是经典费舍信息的量子推广。具体而言,量子费舍信息在估计未知参数?的精度时,给出了理论上可以实现的测量极限,当其值越大时,相应的计量精度也就越高。因此,如何提高量子费舍信息成为要解决的关键问题。众所周知,海森堡不确定原理是量子力学的一个最基本的原理,它告诉我们再精密的仪器设备也无法同时测定两个非对易的量子力学量。尽管如此,我们依然可以在不违背该原理的情况下,通过牺牲一个正交分量的精度来减少另一个正交分量的涨落,这就是大家熟知的“压缩”现象。为了量化压缩,人们提出了包括信息熵压缩在内的各种定义。信息熵压缩是人们测量原子与光场相互作用所产生的压缩效应时的有效理论工具。我们知道,量子系统与周围环境相互作用通常会造成相干性以及压缩特性的损失。因此,研究开放系统中的量子费舍信息以及熵压缩动力学具有现实意义。而光子晶体因具有光子带隙,故系统呈现了许多新奇的量子效应,如量子俘获现象等,有关光子晶体环境的研究是人们感兴趣的另一话题。基于目前的研究背景,本文着重讨论了量子弱测量和测量反转操作对处于光子晶体中的两原子纠缠态的量子费舍信息的影响以及该量子操作对原子熵压缩的调制作用,得到一些有意义的结论。通过分析光子晶体环境中的量子费舍信息动力学行为时发现,不进行弱测量和弱测量反转操作时,参数测量精度可以通过控制失谐量而得到一定程度的提高。当?(27)0时,在各向异性光子晶体中,量子费舍信息随时间衰减,最终趋于一个稳定的值;而在各向同性光子晶体中,量子费舍信息出现了振荡行为,但最终会趋于一个定值。当?(29)0时,不管是各向异性还是各向同性光子晶体,量子费舍信息都很快趋于0。加入最优量子测量操作后,量子费舍信息可得到进一步提高,且弱测量强度越大,量子费舍信息也就越大,相应的参数测量精度也就越高。然而,测量强度越大,其成功的概率就变得越小。通过分析光子晶体环境中的量子熵压缩动力学行为我们发现,当?(29)0时,在各向异性光子晶体中,测量操作有利于熵压缩的存在,但是随着?的增大,弱测量对熵压缩的有利作用逐渐减弱;在各向同性光子晶体中,弱测量强度大于某一个值时,才会对熵压缩产生积极作用。当?(27)0时,在各向异性光子晶体中的熵压缩几乎不受弱测量和测量反转操作的影响,出现等幅振荡行为;在各向同性光子晶体中也会有周期性振荡行为,但是压缩深度不及各向异性光子晶体。
[Abstract]:Metrology is a subject of measuring and measuring errors, and quantum metrology is the product of the combination of quantum mechanics and metrology. Its main task is to realize quantum precision measurement. Because the measurement precision is closely related to the process of parameter measurement, the improvement of measurement precision means the improvement of the accuracy of the experiment. The basic theory, the quantum kcramer (Cram r-Rao) theorem, shows that the minimum boundary of measurement is determined by quantum Fisher information (quantum Fisher information, QFI). The quantum Fisher information here is a quantum generalization of the classical Fisher information. In particular, the quantum Fisher information is theoretically possible to estimate the accuracy of the unknown parameters The measurement limit is achieved, the higher the value is, the higher the corresponding measurement accuracy is. Therefore, how to improve the quantum Fisher information is the key problem to be solved. As we all know, Heisenberg's uncertainty principle is one of the most basic principles of quantum mechanics. It tells us that the more precise instruments can not be measured at the same time two non commutative. In spite of this, we can still reduce the fluctuation of another orthogonal component by sacrificing the accuracy of an orthogonal component without violating the principle. This is known as the "compression" phenomenon. In order to quantify compression, a variety of definitions, including information entropy compression, are proposed. Information entropy compression is proposed. It is an effective theoretical tool when people measure the squeezing effect of the interaction between atoms and light fields. We know that the interaction of the quantum system and the surrounding environment usually causes the loss of the coherence and the compression properties. Therefore, the study of the quantum Fisher information and entropy compression dynamics in the open system is of practical significance. Because of the photonic band gap, the system presents a number of novel quantum effects, such as quantum capture, and the study of the photonic crystal environment is another topic of interest. Based on the current research background, this paper focuses on the quantum weak measurement and the measurement of the amount of entangled states of two atoms in the photonic crystal. The influence of the Fisher information on the quantum operation and the modulation of the quantum operation on the entropy compression of the atom get some meaningful conclusions. By analyzing the dynamic behavior of the quantum Fisher information in the photonic crystal environment, it is found that the parameter measurement accuracy can be obtained by controlling the detuning without the weak measurement and the weak measurement inversion operation. When (27) 0, in the anisotropic photonic crystal, quantum Fisher information attenuates with time and eventually tends to a stable value. In isotropic photonic crystals, quantum Fisher information oscillates, but eventually tends to a fixed value. When? (29) 0, whether it is anisotropic or isotropic photonic crystal, quantum After the Fisher information quickly tends to 0. optimal quantum measurement operations, quantum Fisher information can be further improved, and the greater the intensity of the weak measurement, the greater the quantum Fisher information, the higher the accuracy of the corresponding parameter measurement. However, the greater the intensity of the measurement, the less the probability of its success. The kinetic behavior of quantum entropy compression is found to be beneficial to entropy compression in the anisotropic photonic crystal when (29) 0, but with the increase of the entropy, the beneficial effect of the weak measurement on entropy compression is gradually weakened. In the isotropic photonic crystal, when the weak measurement intensity is greater than a certain value, the entropy compression will be positive. When (27) 0, the entropy compression in the anisotropic photonic crystal is almost unaffected by the influence of the weak measurement and the reversal operation, and there is a constant amplitude oscillation. In the isotropic photonic crystal, there will be periodic oscillation, but the compression depth is less than that of the anisotropic photonic crystal.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O734

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