相干态和薛定谔猫态的直积态在量子相位估值中的潜在应用

发布时间：2019-04-22 11:41

【摘要】：本论文以猫态和相干态的直积态作为主要研究对象,研究光量子态在量子相位测量中的潜在应用,瞄准量子相位估值的核心焦点问题:通过找到合适的量子态,优化力学量以及数据处理过程,使估计量的涨落能够低于标准量子极限(SQL);系统地研究了量子相位测量的基本步骤,双输出测量的基本方法,以及理想情况下的量子Fisher信息(QFI)和经典Fisher信息(CFI)。首先,以相干光和薛定谔猫态的直积态作为干涉仪的输入,研究无损,无噪声的理想条件下系统的量子Fisher信息(QFI):1.给出了相位灵敏度及理想情况下满足相位匹配条件cos[2(θa-θb)]=+1的最优量子Fisher信息的形式,其中θa/b分别是猫态和相干态的相位;2.在实验可行的条件下n～1,找到了最优的nb和na之间的关系;3.证明了奇猫态要比偶猫态具有更好的量子Fisher信息;4.我们也通过数值模拟,证明了影响转化率的主要因素是量子态的引入。此外,我们以相干光为例,研究双输出测量方案中的相位估计量及其涨落[1],并与最近两篇实验结果比较发现:1.采用光的相干态和一个简单高效的零差探测器(homodyne detector)就可得到超分辨的信号,且其相位灵敏度接近散粒噪声极限;2.宇称探测以及零-非零光子计数测量都可以达到超分辨率,相位灵敏度也接近散粒噪声极限。接下来,在理论分析和实验已经结合在一起的基础上,我们将实验中的损耗考虑进去,数值模拟宇称测量和Z探测中的输出信号和灵敏度。通过比较反函数估计法和最大似然估计两种不同的相位估值方法,发现只要测量次数足够多,反函数估计法和最大似然估计法得到的相位估值应该是一样的,相比之下,反函数估计法就会简单很多。在第四章中,我们重新研究了相干态(?)薛定谔猫态的例子,研究光子计数测量中,经典Fisher信息在相位匹配条件下始终等于量子Fisher信息。这一结果与近期成果[2]定性一致。最后,作者给出全文的结论与展望,本文部分结果已经发表.
[Abstract]:In this thesis, the direct product states of cat states and coherent states are taken as the main research objects, and the potential applications of optical quantum states in quantum phase measurement are studied, aiming at the core problem of quantum phase estimation: by finding suitable quantum states, Optimizes mechanical quantities and data processing processes so that the fluctuations of the estimators can be lower than the standard quantum limit of (SQL); The basic steps of quantum phase measurement, the basic method of dual output measurement, and the ideal quantum Fisher information (QFI) and classical Fisher information (CFI). Are systematically studied. Firstly, using the coherent light and the direct product state of the Schrodinger cat state as the input of the interferometer, the quantum Fisher information of the system under the ideal condition of lossless and noise-free is studied. The phase sensitivity and the form of the optimal quantum Fisher information satisfying the phase matching condition cos [2 (胃 a-胃 b)] = 1 are given in this paper, where 胃 a _ (b) is the phase of cat state and coherent state, respectively. Under feasible experimental conditions, the optimal relationship between nb and na is found; 3. It is proved that odd cat states have better quantum Fisher information than even cat states; 4. It is also proved by numerical simulation that the main factor affecting the conversion is the introduction of quantum states. In addition, taking coherent light as an example, we study the phase estimators and their fluctuations in the dual-output measurement scheme [1], and compare with the results of the two recent experiments, we find that: 1. The super-resolution signal can be obtained by using the coherent state of light and a simple and efficient zero-difference detector (homodyne detector), and the phase sensitivity of the signal is close to the limit of scattered noise. Parity detection and zero-non-zero photon counting can achieve super-resolution and phase sensitivity is close to the limit of scattered noise. Then, on the basis of theoretical analysis and experiment, we take the loss into account and simulate the output signal and sensitivity in parity measurement and Z detection. By comparing two different phase estimation methods, the inverse function estimation method and the maximum likelihood estimation method, it is found that the phase estimation obtained by the inverse function estimation method and the maximum likelihood estimation method should be the same as that obtained by the maximum likelihood estimation method as long as the number of measurements is enough. The inverse function estimation method is much simpler. In chapter 4, we re-examine the coherent state (?) In the case of Schrodinger cat state, the classical Fisher information in photon counting measurement is always equal to the quantum Fisher information under the condition of phase matching. This result is qualitatively consistent with recent results [2]. Finally, the author gives the conclusions and prospects of this paper, some of the results have been published.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O431.2

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