本文選題：量子費(fèi)舍信息 + 熵壓縮　； 參考：《山西大學(xué)》2017年碩士論文

【摘要】：計(jì)量學(xué)是研究測(cè)量及測(cè)量誤差的一門學(xué)科,而量子計(jì)量學(xué)是計(jì)量學(xué)與量子力學(xué)相互結(jié)合的產(chǎn)物,其主要任務(wù)是實(shí)現(xiàn)量子精密測(cè)量。由于測(cè)量精度與參數(shù)測(cè)量過程密切相關(guān),因此測(cè)量精度的提高就意味著實(shí)驗(yàn)準(zhǔn)確性的提高。從參數(shù)估計(jì)的基本理論——量子克拉美羅(Cramér-Rao)定理可知,測(cè)量的最低界限由量子費(fèi)舍信息(quantum Fisher information,QFI)確定,這里的量子費(fèi)舍信息是經(jīng)典費(fèi)舍信息的量子推廣。具體而言,量子費(fèi)舍信息在估計(jì)未知參數(shù)?的精度時(shí),給出了理論上可以實(shí)現(xiàn)的測(cè)量極限,當(dāng)其值越大時(shí),相應(yīng)的計(jì)量精度也就越高。因此,如何提高量子費(fèi)舍信息成為要解決的關(guān)鍵問題。眾所周知,海森堡不確定原理是量子力學(xué)的一個(gè)最基本的原理,它告訴我們?cè)倬艿膬x器設(shè)備也無(wú)法同時(shí)測(cè)定兩個(gè)非對(duì)易的量子力學(xué)量。盡管如此,我們依然可以在不違背該原理的情況下,通過犧牲一個(gè)正交分量的精度來(lái)減少另一個(gè)正交分量的漲落,這就是大家熟知的“壓縮”現(xiàn)象。為了量化壓縮,人們提出了包括信息熵壓縮在內(nèi)的各種定義。信息熵壓縮是人們測(cè)量原子與光場(chǎng)相互作用所產(chǎn)生的壓縮效應(yīng)時(shí)的有效理論工具。我們知道,量子系統(tǒng)與周圍環(huán)境相互作用通常會(huì)造成相干性以及壓縮特性的損失。因此,研究開放系統(tǒng)中的量子費(fèi)舍信息以及熵壓縮動(dòng)力學(xué)具有現(xiàn)實(shí)意義。而光子晶體因具有光子帶隙,故系統(tǒng)呈現(xiàn)了許多新奇的量子效應(yīng),如量子俘獲現(xiàn)象等,有關(guān)光子晶體環(huán)境的研究是人們感興趣的另一話題�；谀壳暗难芯勘尘�,本文著重討論了量子弱測(cè)量和測(cè)量反轉(zhuǎn)操作對(duì)處于光子晶體中的兩原子糾纏態(tài)的量子費(fèi)舍信息的影響以及該量子操作對(duì)原子熵壓縮的調(diào)制作用,得到一些有意義的結(jié)論。通過分析光子晶體環(huán)境中的量子費(fèi)舍信息動(dòng)力學(xué)行為時(shí)發(fā)現(xiàn),不進(jìn)行弱測(cè)量和弱測(cè)量反轉(zhuǎn)操作時(shí),參數(shù)測(cè)量精度可以通過控制失諧量而得到一定程度的提高。當(dāng)?(27)0時(shí),在各向異性光子晶體中,量子費(fèi)舍信息隨時(shí)間衰減,最終趨于一個(gè)穩(wěn)定的值;而在各向同性光子晶體中,量子費(fèi)舍信息出現(xiàn)了振蕩行為,但最終會(huì)趨于一個(gè)定值。當(dāng)?(29)0時(shí),不管是各向異性還是各向同性光子晶體,量子費(fèi)舍信息都很快趨于0。加入最優(yōu)量子測(cè)量操作后,量子費(fèi)舍信息可得到進(jìn)一步提高,且弱測(cè)量強(qiáng)度越大,量子費(fèi)舍信息也就越大,相應(yīng)的參數(shù)測(cè)量精度也就越高。然而,測(cè)量強(qiáng)度越大,其成功的概率就變得越小。通過分析光子晶體環(huán)境中的量子熵壓縮動(dòng)力學(xué)行為我們發(fā)現(xiàn),當(dāng)?(29)0時(shí),在各向異性光子晶體中,測(cè)量操作有利于熵壓縮的存在,但是隨著?的增大,弱測(cè)量對(duì)熵壓縮的有利作用逐漸減弱;在各向同性光子晶體中,弱測(cè)量強(qiáng)度大于某一個(gè)值時(shí),才會(huì)對(duì)熵壓縮產(chǎn)生積極作用。當(dāng)?(27)0時(shí),在各向異性光子晶體中的熵壓縮幾乎不受弱測(cè)量和測(cè)量反轉(zhuǎn)操作的影響,出現(xiàn)等幅振蕩行為;在各向同性光子晶體中也會(huì)有周期性振蕩行為,但是壓縮深度不及各向異性光子晶體。
[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.
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O734

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 馮晉霞;張寬收;;連續(xù)變量多模壓縮態(tài)光場(chǎng)[J];量子光學(xué)學(xué)報(bào);2011年03期

2 劉小娟;周元俊;方卯發(fā);;Optimal entropy squeezing sudden generation and its control for an effective two-level moving atom entanglement with the two-mode coherent fields[J];Chinese Physics B;2009年06期

3 張劍;邵彬;鄒健;;Entropy squeezing for a two-level atom in two-mode Raman coupled model with intrinsic decoherence[J];Chinese Physics B;2009年04期

4 段路明,郭光燦;量子信息講座第一講 量子計(jì)算機(jī)[J];物理;1998年01期

相關(guān)碩士學(xué)位論文 前1條

1 王寧;光子晶體中的量子糾纏和量子計(jì)量問題[D];山西大學(xué);2016年

，

本文編號(hào)：2046335