Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model

doi:10.1088/1674-1056/19/9/090311

Abstract This paper shows that a proposal for implementing all possible two-operator positive-operator-value measurements of single spin qubit can be obtained via introducing another spin qubit as ancilla. The realization process is accomplished from the free evolution of the Heisenberg XX model by considering nearest-neighbour spin interaction. A controlled-NOT gate, which is a significant operator for this scheme is also constructed and the generalisation to multiple-operator is considered finally.

Keywords: positive-operator-value measurements single spin qubit Heisenberg model

Received: 02 December 2009
Revised: 18 January 2010
Accepted manuscript online:

PACS:	0365
	4250

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60667001).

Cite this article:

Cheng Liu-Yong(程留永), Shao Xiao-Qiang(邵晓强), Zhang Shou(张寿), and Yeon Kyu-Hwang Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model 2010 Chin. Phys. B 19 090311

[1]	Neumann J V 1955 Mathematical Foundations of Quantum Mechanics (Princeton, New York: Princeton UP)
[2]	Helstrom C 1976 Quantum Detection and Estimation Theory (New York: Academic Press)
[3]	Franke-Arnold S, Andersson E, Barnett S M and Stenholm S 2001 emphPhys. Rev. A 63 052301
[4]	Han Y, Wu C W, Wu W, Chen P X and Li C Z 2009 emphChin. Phys. B 18 3215
[5]	Sun Y, Hillery M and Bergou J A 2001 emphPhys. Rev. A 64 022311
[6]	Ahnert S E and Payne M C 2005 emphPhys. Rev. A 71 012330
[7]	Lin Q 2009 emphChin. Phys. B 18 51
[8]	Browne D E and Rudolph T 2005 emphPhys. Rev. Lett. 95 010501
[9]	Barrett S D and Kok P 2005 emphPhys. Rev. A 71 060310
[10]	Zheng S B and Guo G C 2000 emphPhys. Rev. Lett. 85 2392
[11]	Wang H F and Zhang S 2008 emphChin. Phys. B 17 1165
[12]	Bulaevskii L and Ortiz G 2003 emphPhys. Rev. Lett. 90 040401
[13]	Bulaevskii L, Hrucheckska M, Shnirman A, Smith D and Makhlin Y 2004 emphPhys. Rev. Lett. 92 177001
[14]	Neumark M A and Akad I 1940 emphNauk SSSR, Ser. Mat. 4 277
[15]	Andersson E and Oi D K L 2008 emphPhys. Rev. A 77 052104
[16]	Wang G and Ying M 2006 arXiv: quant-ph/0608235
[17]	Chen P X, Bergou J A, Zhu S Y and Guo G C 2007 emphPhys. Rev. A 76 060303
[18]	Yung M H, Leung D W and Bose S 2004 emphQuantum Inf. Comput. 4 174
[19]	Dieks D 1988 emphPhys. Lett. A 126 303
[20]	Peres A 1988 emphPhys. Lett. A 128 19
[21]	Lu J, Zhou L and Kuang L M 2006 emphChin. Phys. 15 1941
[22]	Ekert A K, Huttner B, Palma G M and Peres A 1994 emphPhys. Rev. A 50 1047
[23]	Chefles A and Barnett S M 1998 emphPhys. Lett. A 250 223 endfootnotesize

[1]	Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J₁-J₂ Heisenberg model He-Yu Lin(林赫羽), Rong-Qiang He(贺荣强), and Zhong-Yi Lu(卢仲毅). Chin. Phys. B, 2022, 31(8): 080203.
[2]	Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[3]	Magnetic excitations of diagonally coupled checkerboards Tingting Yan(颜婷婷), Shangjian Jin(金尚健), Zijian Xiong(熊梓健), Jun Li(李军), and Dao-Xin Yao(姚道新). Chin. Phys. B, 2021, 30(10): 107505.
[4]	Lifshitz transition in triangular lattice Kondo-Heisenberg model Lan Zhang(张欄), Yin Zhong(钟寅), Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2020, 29(7): 077102.
[5]	Exciton dynamics in different aromatic hydrocarbon systems Milica Rutonjski†, Petar Mali, Slobodan Rado\v sevi\'c, Sonja Gombar, Milan Panti\'c, and Milica Pavkov-Hrvojevi\'c. Chin. Phys. B, 2020, 29(10): 107103.
[6]	Quantum steering in Heisenberg models with Dzyaloshinskii-Moriya interactions Hui-Zhen Li(李慧贞), Rong-Sheng Han(韩榕生), Ye-Qi Zhang(张业奇), Liang Chen(陈亮). Chin. Phys. B, 2018, 27(12): 120304.
[7]	Quantum correlation dynamics in a two-qubit Heisenberg XYZ model with decoherence Yang Guo-Hui (杨国晖), Zhang Bing-Bing (张冰冰), Li Lei (李磊). Chin. Phys. B, 2015, 24(6): 060302.
[8]	Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field Li Lei (李磊), Yang Guo-Hui (杨国晖). Chin. Phys. B, 2014, 23(7): 070306.
[9]	A thermal entangled quantum refrigerator based on a two-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction in an external magnetic field Wang Hao (汪浩), Wu Guo-Xing (吴国兴). Chin. Phys. B, 2013, 22(5): 050512.
[10]	Entanglement dynamics of two qubits coupled by Heisenberg XY interaction under a nonuniform magnetic field in a spin bath Zhou Feng-Xue(周凤雪), Zhang Li-Da(张理达), Qi Yi-Hong(祁义红), Niu Yue-Ping(钮月萍), Zhang Jing-Tao(张敬涛), and Gong Shang-Qing(龚尚庆) . Chin. Phys. B, 2011, 20(8): 080302.
[11]	Thermal quantum discord in Heisenberg models with Dzyaloshinski–Moriya interaction Wang Lin-Cheng(王林成), Yan Jun-Yan(闫俊彦), and Yi Xue-Xi(衣学喜) . Chin. Phys. B, 2011, 20(4): 040305.
[12]	Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii－Moriya interaction Chen Tao(陈涛), Huang Yan-Xia(黄燕霞), Shan Chuan-Jia(单传家), Li Jin-Xing(李金星), Liu Ji-Bing(刘继兵), and Liu Tang-Kun(刘堂昆). Chin. Phys. B, 2010, 19(5): 050302.
[13]	Pairwise thermal entanglement in a three-qubit Heisenberg XX model with a nonuniform magnetic field and Dzyaloshinski–Moriya interaction Ren Jin-Zhong(任金忠), Shao Xiao-Qiang(邵晓强), Zhang Shou(张寿), and Yeon Kyu-Hwang. Chin. Phys. B, 2010, 19(10): 100307.
[14]	Tunable thermal entanglement in an effective spin-star system using coupled microcavities Yang Wan-Li(杨万里), Wei Hua(魏华), Feng Mang(冯芒), and An Jun-Hong(安钧鸿). Chin. Phys. B, 2009, 18(9): 3677-3686.
[15]	Effects of Dzyaloshinski--Moriya interaction and intrinsic decoherence on teleportation via a two-qubit Heisenberg XYZ model Hu Xiao-Mian(胡小勉) and Liu Jin-Ming(刘金明). Chin. Phys. B, 2009, 18(2): 411-417.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model

Cite this article:

Online attention