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Quantum Information Processing
Published in: Quantum Information Processing 11/2017

01-11-2017

Coherence of one-dimensional quantum walk on cycles

Authors: Zhimin He, Zhiming Huang, Lvzhou Li, Haozhen Situ

Published in: Quantum Information Processing | Issue 11/2017

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Abstract

Quantum coherence plays a central role in quantum mechanics and provides essential power for quantum information processing. In this paper, we study the dynamics of the \(l_1\) norm coherence in one-dimensional quantum walk on cycles for two initial states. For the first initial state, the walker starts from a single position. The coherence increases with the number of steps at the beginning and then fluctuates over time after approaching to saturation. The coherence with odd number of sites is much larger than that with even number of sites. Another initial state, i.e., the equally superposition state, is also considered. The coherence of the whole system is proved to be \(N-1\) (\(2N-1\)) for any odd (even) time step where N is the number of sites. We also investigate the influence of two unitary noises, i.e., noisy Hadamard operator and broken link, on the coherence evolution.
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Footnotes
1
By curve fitting, we have \(C(|{\varPsi }(t)\rangle )=1.527 t^{0.9405}\) and \(C(Tr_C(|{\varPsi }(t)\rangle ))=0.5818 t^{0.9626}\).
 
Literature
1.
Barber, M.N., Ninham, B.W.: Random and Restricted Walks: Theory and Applications. CRC Press, Boca Raton (1970)MATH
2.
Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993)ADSCrossRef
3.
Kendon, V., Tregenna, B.: Decoherence can be useful in quantum walks. Phys. Rev. A 67, 042315 (2003)ADSCrossRef
4.
Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. 50–59. ACM (2001)
5.
Maloyer, O., Kendon, V.: Decoherence versus entanglement in coined quantum walks. New J. Phys. 9, 87 (2007)ADSCrossRef
6.
7.
Du, Y.M., Lu, L.H., Li, Y.Q.: Switching effect of the side chain on quantum walks on triple graphs. Phys. Rev. A 92, 012309 (2015)ADSCrossRef
8.
Oliveira, A., Portugal, R., Donangelo, R.: Decoherence in two-dimensional quantum walks. Phys. Rev. A 74, 012312 (2006)ADSCrossRef
9.
Shapira, D., Biham, O., Bracken, A., Hackett, M.: One-dimensional quantum walk with unitary noise. Phys. Rev. A 68, 062315 (2003)ADSCrossRefMathSciNet
10.
Rodriguez, J.P., Li, Z.J., Wang, J.B.: Discord and entanglement of two-particle quantum walk on cycle graphs. Quantum Inf. Process. 14, 119 (2015)ADSCrossRefMATHMathSciNet
11.
Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., Osellame, R.: Two-particle Bosonic–Fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012)ADSCrossRef
12.
Xue, P., Zhang, R., Bian, Z.H., Zhan, X., Qin, H., Sanders, B.C.: Localized state in a two-dimensional quantum walk on a disordered lattice. Phys. Rev. A 92, 042316 (2015)ADSCrossRef
13.
Xu, Y.Z., Guo, G.D., Lin, S.: One-dimensional three-state quantum walk with single-point phase defects. Int. J. Theor. Phys. 55, 4060 (2016)CrossRefMATHMathSciNet
14.
Romanelli, A., Siri, R., Abal, G., Auyuanet, A., Donangelo, R.: Decoherence in the quantum walk on the line. Physica A 347, 137 (2005)ADSCrossRefMathSciNet
15.
Zhang, Y.C., Bao, W.S., Wang, X., Fu, X.Q.: Decoherence in optimized quantum random-walk search algorithm. Chin. Phys. B 24, 080307 (2015)ADSCrossRef
16.
Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)ADSCrossRef
17.
Potocek, V., Gabris, A., Kiss, T., Jex, I.: Optimized quantum random-walk search algorithms on the hypercube. Phys. Rev. A 79, 012325 (2009)ADSCrossRef
18.
Xue, X.L., Chen, H.W., Liu, Z.H., Zhang, B.B.: Search algorithm of structure anomalies in complete graph based on scattering quantum walk. Acta Phys. Sin. 65, 080302 (2016)
19.
Xue, X.L., Chen, H.W., Liu, Z.H.: Finding structural anomalies in complete graphs using scattering quantum walks. Int. J. Quantum Inf. 14, 1650035 (2016)CrossRefMATH
20.
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
21.
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADSCrossRef
22.
Yao, Y., Xiao, X., Ge, L., Sun, C.P.: Quantum coherence in multipartite systems. Phys. Rev. A 92, 022112 (2015)ADSCrossRef
23.
Yao, Y., Dong, G.H., Xiao, X., Sun, C.P.: Frobenius-norm-based measures of quantum coherence and asymmetry. Sci. Rep. 6, 32010 (2016)ADSCrossRef
24.
Wang, J.C., Tian, Z.H., Jing, J.L., Fan, H.: Irreversible degradation of quantum coherence under relativistic motion. Phys. Rev. A 93, 062105 (2016)ADSCrossRef
25.
Liu, X.B., Tian, Z.H., Wang, J.C., Jing, J.L.: Protecting quantum coherence of two-level atoms from vacuum fluctuations of electromagnetic field. Ann. Phys. 366, 102 (2016)ADSCrossRefMATHMathSciNet
26.
27.
28.
29.
30.
Huang, Z.M., Situ, H.Z.: Dynamics of quantum correlation and coherence for two atoms coupled with a bath of fluctuating massless scalar field. Ann. Phys. 377, 484–492 (2017)ADSCrossRefMATH
31.
Huang, Z.M., Situ, H.Z.: Optimal protection of quantum coherence in noisy environment. Int. J. Theor. Phys. 56, 503 (2017)CrossRefMATH
32.
Huang, Z.M., Situ, H.Z., Zhang, C.: Quantum coherence and correlation in spin models with Dzyaloshinskii–Moriya interaction. Int. J. Theor. Phys. 56, 2178 (2017)CrossRefMathSciNet
33.
Huang, Z.M., Rong, Z.B., Zou, X.F., Situ, H.Z., Zhao, L.H.: Protecting qutrit quantum coherence. Int. J. Theor. Phys. 56, 2540 (2017)CrossRefMathSciNet
34.
Huang, Z.M., Situ, H.Z.: Non-Markovian dynamics of quantum coherence of two-level system driven by classical field. Quantum Inf. Process. 16, 222 (2017)ADSCrossRefMathSciNet
35.
Hillery, M.: Coherence as a resource in decision problems: the Deutsch–Jozsa algorithm and a variation. Phys. Rev. A 93, 012111 (2016)ADSCrossRef
36.
Ma, J.J., Yadin, B., Girolami, D., Vedral, V., Gu, M.: Converting coherence to quantum correlations. Phys. Rev. Lett. 116, 160407 (2016)ADSCrossRef
37.
Matera, J.M., Egloff, D., Killoran, N., Plenio, M.B.: Coherent control of quantum systems as a resource theory. Quantum Sci. Technol. 1, 01LT01 (2016)CrossRef
38.
Metadata
Title
Coherence of one-dimensional quantum walk on cycles
Authors
Zhimin He
Zhiming Huang
Lvzhou Li
Haozhen Situ
Publication date
01-11-2017
Publisher
Springer US
Published in
Quantum Information Processing / Issue 11/2017
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-017-1724-6

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