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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 |
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Abstract 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.
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Received: 11 February 2018
Revised: 17 June 2018
Accepted manuscript online:
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PACS:
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03.67.-a
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(Quantum information)
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03.65.Wj
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(State reconstruction, quantum tomography)
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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Fund: Project supported partially by the National Key Research and Development Program of China (Grant No. 2016YFB1000902), the National Natural Science Foundation of China (Grant No. 61472412), and the Program for Creative Research Group of the National Natural Science Foundation of China (Grant No. 61621003). |
Corresponding Authors:
Yun Shang
E-mail: shangyun602@163.com
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Cite this article:
Yu Wang(王宇), Yun Shang(尚云) Two-qubit pure state tomography by five product orthonormal bases 2018 Chin. Phys. B 27 100306
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[1] |
Wootters W K and Zurek W H 1982 Nature 299 802
|
[2] |
Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
|
[3] |
Gross D, Liu Y K, Flammia S T, Becker S and Eisert J 2010 Phys. Rev. Lett. 105 150401
|
[4] |
Ma X, Jackson T, Zhou H, Chen J X, Lu D W, Mazurek M D, Fisher K A G, Peng X H, Kribs D, Resch K J, Ji Z F, Zeng B and Laflamme R 2016 Phys. Rev. A 93 032140
|
[5] |
Yan F, Yang M and Cao Z L 2010 Phys. Rev. A 82 044102
|
[6] |
Adamson R B A and Steinberg A M 2010 Phys. Rev. Lett. 105 030406
|
[7] |
Lima G, Neves L, Guzmán R, Gómez E S, Nogueira W A T, Delgado A, Vargas A and Saavedra C 2011 Opt. Express 19 3542
|
[8] |
Giovannini D, Romero J, Leach J, Dudley A, Forbes A and Padgett M J 2013 Phys. Rev. Lett. 110 143601
|
[9] |
Daniel F V J, Paul G K, William J M and Andrew G W 2001 Phys. Rev. A 64 052312
|
[10] |
Carmeli C, Heinosaari T, Schultz J and Toigo A 2015 Euro. Phys. J. D 69 179
|
[11] |
Goyeneche D, Caňas G, Etcheverry S, Gómez E S, Xavier G B, Lima G and Delgado A 2015 Phys. Rev. Lett. 115 090401
|
[12] |
Carmeli C, Heinosaari T, Kech M, Schultz J and Toigo A 2016 Europhys. Lett. 115 30001
|
[13] |
Renes J M, Blume-Kohout R, Scott A J and Caves C M 2004 J. Math. Phys. 45 2171
|
[14] |
Řeháček J, Englert B G and Kaszlikowski D 2004 Phys. Rev. A 70 052321
|
[15] |
Kalev A, Shang J W and Englert B G 2012 Phys. Rev. A 85 052115
|
[16] |
Band W and Park J 1970 Found. Phys. 1 133
|
[17] |
Park J and Band W 1971 Found. Phys. 1 211
|
[18] |
Lvovsky A I and Raymer M G 2009 Rev. Mod. Phys. 81 299
|
[19] |
Yin Q, Xiang G Y, Li Ch F and Guo G C 2017 Chin. Phys. Lett. 34 030301
|
[20] |
Blume-Kohout R 2010 New J. Phys. 12 043034
|
[21] |
Baldwin C H, Deutsch I H and Kalev A 2016 Phys. Rev. A 93 052105
|
[22] |
Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge:Cambridge University) pp. 172, 389, 398
|
[23] |
Pauli W 1933 Die allgemeinen Prinzipen der Wellenmechanik, Vol. 24 (Berlin:Springer-Verlag)
|
[24] |
Peres A 1993 Quantum Theory:Concepts and Methods (Dordrecht:Kluwer Academic, The Netherlands), POVMs are discussed in Sections 9-5 and 9-6, and PSI-complete measurements in Section 3-5.
|
[25] |
Flammia S T, Silberfarb A and Caves C M 2005 Found. Phys. 35 1985
|
[26] |
Moroz B Z 1983 Int. J. Theor. Phys. 22 329
|
[27] |
Moroz B Z 1994 Theor. Math. Phys. 101 1200
|
[28] |
Heinosaari T, Mazzarella L and Wolf M M 2013 Commun. Math. Phys. 318 355
|
[29] |
Jaming P 2014 Appl. Comput. Harmon. A 37 413
|
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