我们通过计算机模拟得到相位抖动情况下“光学薛定谔”猫态的正交分量测量集,利用极大似然估计进行量子态重构,获得“光学薛定谔”猫态的Wigner函数。研究了“光学薛定谔”猫态的保真度及Wigner函数相空间原点值W(0,0)随相位抖动的变化,发现保真度随相位抖动幅度的增大而降低,而W(0,0)值则对相位抖动不敏感。另外,我们在不同的输入态压缩纯度和压缩度下,分析了相位抖动对“光学薛定谔”猫态保真度的影响,结果表明:压缩纯度越大,相位抖动对保真度的影响越小;压缩度越大,保真度对相位抖动越敏感。

Schrodinger cat state is a continuous variable quantum state,and it plays an important role in the research of fundamental physical problems and quantum information.Cat state is a superposition of two coherent states with identical amplitudes and opposite phases,which can be used as an encoded qubit for quantum computing,quantum repeater as well as quantum precision measurement.Generally Cat state is prepared experimentally by subtracting a photon from vacuum squeezed state. The generation of a Cat state is predicted by the click of a single photon detector,while the quadrature components are measured with the balance homodyne detection. Because the noise distribution of the quadrature components of a Cat state is dependent on phase,the phase jitter in homodyne detection system is an important factor on the quality of the prepared Cat state. We study the impact of phase jitter in homodyne detection on the preparation of Cat state. At first,in the case of stable phases we obtain the analytic expression of the marginal distribution of the quadrature noise of a Cat state,and get the measurement set of the quadrature components by computer simulation. Then the measurement set under the condition of phase jitter are acquired by means of transforming the marginal distribution, and the Wigner function of the quantum state is reconstructed using Maximum Likelihood Estimation. We analyze the fidelity of Cat state as well as the origin value W(0,0) of the Wigner function as a function of phase jitter amplitude. It shows that the fidelity decreases with increasing of phase jitter amplitude while W(0,0) value is insensitive to phase jitter. Furthermore, the impact of phase jitter on fidelity of Cat state is analyzed for different squeezing degrees and squeezing purities of the input states. The results indicate that the lower squeezing degree or higher squeezing purity, the smaller the influence of phase jitter on fidelity. Either a higher squeezing degree or a smaller squeezing purity will result in a more significant difference in the noise distribution of the quadrature components between the phases 0° and 90°. When phase jitter occurs, the quadrature components are redistributed in the range of phase jitter. If the distribution difference between different phases is significant, the decreasing of fidelity resulting from phase jitter will be obvious, so the fidelity of Cat state is more insensitive to the phase jitter when the squeezing degree is lower or the squeezing purity is higher. The above work can provide a theoretical guidance for the experimental preparation of cat state with high fidelity.