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- Title
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.
- Authors
杨靖北; 丛爽; 陈鼎
- Abstract
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 ≤ l ≤ 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%.
- Subjects
QUANTUM theory; QUANTUM mechanics; TOMOGRAPHY; PAULI matrices; EIGENVALUES
- Publication
Control Theory & Applications / Kongzhi Lilun Yu Yinyong, 2017, Vol 34, Issue 11, p1514
- ISSN
1000-8152
- Publication type
Article
- DOI
10.7641/CTA.2017.70614