| 引用本文: | 杨靖北,丛爽,陈鼎.基于两步测量方法及其最少观测次数的任意量子纯态估计[J].控制理论与应用,2017,34(11):1514~1521.[点击复制] |
| YANG Jing-bei,CONG Shuang,CHEN Ding.Estimation of arbitrary quantum pure states based on the two-step measurement method and the minimum observations[J].Control Theory and Technology,2017,34(11):1514~1521.[点击复制] |
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| 基于两步测量方法及其最少观测次数的任意量子纯态估计 |
| Estimation of arbitrary quantum pure states based on the two-step measurement method and the minimum observations |
| 摘要点击 1656 全文点击 1170 投稿时间：2017-08-31 修订日期：2017-12-09 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2017.70614 |
| 2017,34(11):1514-1521 |
| 中文关键词 量子状态估计 两步测量方法 压缩传感 观测算符 |
| 英文关键词 quantum state estimation two-step measurement method compressed sensing observables |
| 基金项目 国家自然科学基金项目(61573330, 61720106009), 天地一体化信息技术国家重点实验室开放基金项目(2015 SGIIT KFJJ DH 04) |
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| 中文摘要 |
| 量子状态层析所需要的完备观测次数d2(d = 2n)随着状态的量子位数n的增加呈指数增长, 这使得对高维
量子态的层析变得十分困难. 本文提出一种基于两步测量的量子态估计方法, 可以对任意量子纯态的估计提供最少
的观测次数. 本文证明: 当选择泡利观测算符, 采用本文所提出的量子态估计方法对d = 2n维希尔伯特空间中的任
意n量子位纯态进行重构时, 如果为本征态, 那么所需最少观测次数me
min仅为me
min = n; 对于包含l(2 6 l 6 d)个
非零本征值的叠加态, 重构所需最少观测次数ms
min满足ms
min = d + 2l ?? 3, 此数目远小于压缩传感理论给出的量
子态重构所需测量配置数目O(rd log d), 以及目前已发表论文给出的纯态唯一确定所需最少观测次数4d ?? 5. 同时
给出最少观测次数对应的最优观测算符集的构建方案, 并通过仿真实验对本文所提出的量子态估计方法进行验证,
实验中重构保真度均达到97%以上. |
| 英文摘要 |
| The number of complete observables required in quantum state tomography is d2(d = 2n), which increases
exponentially with the qubit number n of the quantum system, makes the reconstruction of the high dimensional quantum
state become very difficult. In this paper, we propose a quantum two-step measurement method of the estimation of
arbitrary quantum pure states with the minimum number of observables. We prove when choosing the observables of Pauli
operators and the two steps measurement method proposed in this paper, the minimum number of observables required
for the estimation of an n-qubit eigenstate is me
min = n, and the minimum number of a superposition state consisting
of l(2 6 l 6 d) nonzero eigenvalues satisfies ms
min = d + 2l ?? 3. Either the number of eigenstate or super-position
state is far less than the number of measurement configurations required by compressive sensing O(rd log d), and the
minimum number of observables for pure states uniquely determination 4d??5 in published papers up to now. We also give
the method of selecting the corresponding observable sets, called the optimal observable set in this paper. Mathematical
simulation experiments are carried out to validate the method of pure state reconstruction based on adaptive measurements.
The fidelities in our experiments are all over 97%. |
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