中国物理B ›› 2018, Vol. 27 ›› Issue (10): 100306-100306.doi: 10.1088/1674-1056/27/10/100306
• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇 下一篇
Two-qubit pure state tomography by five product orthonormal bases
Yu Wang(王宇), Yun Shang(尚云)
- 1 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China;
4 MDIS, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China
Two-qubit pure state tomography by five product orthonormal bases
Yu Wang(王宇)1,2, Yun Shang(尚云)1,2,3,4
- 1 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China;
4 MDIS, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China
摘要：
In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {|0><0|,|1><1|}. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases B1,B2,B3. Denote the unitary transition matrices from B1 to B2,B3 as U1 and U2. All 32 elements of matrices U1 and U2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.
中图分类号: (Quantum information)
- 03.67.-a