Compressed Sensing Quantum State Tomography Assisted by Adaptive Design
Qi Yin1,2 , Guo-Yong Xiang1,2** , Chuan-Feng Li1,2 , Guang-Can Guo1,2
1 Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 2300262 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026
Abstract ：The recently proposed compressed sensing (CS) method sheds light on quantum state tomography of multi-qubit systems with low rank, which greatly reduces the complexity of measurement and computation. However, the restricted isometry property requirement of CS is difficult to be promised or verified in practice, which makes this method probably assign unreasonable results. In regard to this problem, we adopt a two-step procedure and implement an adaptive strategy to update measurement operators based on the measurement results of the first step for CS, which not only serves as a way to verify the estimate but also improves the accuracy of tomography. Our numerical simulations manifest that our adaptive protocol can reduce about half of the infidelity of non-adaptive protocol and is still efficient even when the rank of the state is slightly high, which would greatly benefit multi-qubit state tomography in future experiments.
收稿日期: 2018-02-12
出版日期: 2018-06-24
:
03.67.-a
(Quantum information)
03.65.Wj
(State reconstruction, quantum tomography)
42.50.Dv
(Quantum state engineering and measurements)
[1] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [2] Smithey D T, Beck M, Raymer M G and Faridani A 1993 Phys. Rev. Lett. 70 1244 [3] James D F V, Kwiat P G, Munro W J and White A G 2001 Phys. Rev. A 64 052312 [4] Paris M and Řeháček J 2004 Quantum State Estimation (Berlin: Springer) vol 649 [5] Qi B, Hou Z B, Li L, Dong D Y, Xiang G Y and Guo G C 2013 Sci. Rep. 3 3496 [6] Häffner H, Hänsel W, Roos C F, Benhelm J and Chekal-kar D 2005 Nature 438 643 [7] Hou Z B, Zhong H S, Tian Y, Dong D Y, Qi B, Li L, Wang Y L, Nori F, Xiang G Y, Li C F and Guo G C 2016 New J. Phys. 18 083036 [8] Bialczak R C, Ansmann M, Hofheinz M, Lucero E and Neeley M 2010 Nat. Phys. 6 409 [9] Cramer M, Plenio M, Flammia S, Somma R, Gross D, Bartlett S, Cardinal O L, Poulin D and Liu Y K 2010 Nat. Commun. 1 149 [10] Zhao Y Y, Hou Z B, Xiang G Y, Han Y J, Li C F and Guo G C 2017 Opt. Express 25 9010 [11] Gross D, Liu Y K, Flammia S T, Becker S and Eisert J 2010 Phys. Rev. Lett. 105 150401 [12] Liu W T, Zhang T, Liu J Y, Chen P X and Yuan J M 2012 Phys. Rev. Lett. 108 170403 [13] Flammia S T, Gross D, Liu Y K and Eisert J 2012 New J. Phys. 14 095022 [14] Shabani A, Kosut R L, Mohseni M, Rabitz H, Broome M A, Almeida M P, Fedrizzi A and White A G 2011 Phys. Rev. Lett. 106 100401 [15] Howl, G A, Schneeloch J, Lum D J and Howell J C 2014 Phys. Rev. Lett. 112 253602 [16] Sugiyama T, Turner P S and Murao M 2012 Phys. Rev. A 85 052107 [17] Huszár F and Houlsby N M T 2012 Phys. Rev. A 85 052120 [18] Mahler D H, Rozema L A, Darabi A, Ferrie C, Blume-Kohout R and Steinberg A M 2013 Phys. Rev. Lett. 111 183601 [19] Hou Z B, Zhu H J, Xiang G Y, Li C F and Guo G C 2016 npj Quantum Inf. 2 16001 [20] Qi B, Hou Z B, Wang Y Y, Dong D Y, Zhong H S, Li L, Xiang G Y, Wiseman H M, Li C F and Guo G C 2017 npj Quantum Inf. 3 19 [21] Donoho D 2006 IEEE Trans. Inf. Theory 52 1289 [22] Candes E J and Wakin M B 2008 IEEE Signal Process. Mag. 25 21 [23] Kalev A, Kosut R L and Deutsch I H 2015 npj Quantum Inf. 1 15018 [24] Steffens A, Riofrio C, McCutcheon W, Roth I, Bell B A, McMillan A, Tame M S, Rarity J G and Eisert J 2016 arXiv:1611.01189 [25] Blume-Kohout R 2010 Phys. Rev. Lett. 105 200504 [26] Blume-Kohout R 2010 New J. Phys. 12 043034 [27] Barkan O, Weill J, Averbuch A and Dekel S 2013 Adaptive Compressed Tomography Sensing (IEEE Conference on Computer Vision and Pattern Recognition) [28] Malloy M L and Nowak R D 2014 IEEE Trans. Inf. Theory 60 4001 [29] Zheng K, Li K Z and Cong S 2016 Sci. Rep. 6 38497 [30] Yin Q, Li L, Xiang X, Xiang G Y, Li C F and Guo G C 2017 Phys. Rev. A 95 012129 [31] Grant M, Boyd S 2014 CVX: Matlab Software for Disciplined Convex Programming and Version 2. 1 [32] Li K Z, Zhang H, Kuang S, Meng F F and Cong S 2016 Quantum Inf. Process. 15 2343 [33] Riofrío C A, Gross D, Flammia S T, Monz T, Nigg D, Blatt R and Eisert J 2017 Nat. Commun. 8 15305
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2018, Vol. 35 
