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Published in: Quantum Information Processing 6/2013

01-06-2013

Analysis of the two-particle controlled interacting quantum walks

Authors: Dan Li, Jie Zhang, Xiu-Wen Ma, Wei-Wei Zhang, Qiao-Yan Wen

Published in: Quantum Information Processing | Issue 6/2013

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Abstract

We have recently proposed the two-particle controlled interacting quantum walks for building quantum Hash schemes (Li et al. Quantum Inf Proc, 2012. doi:10.​1007/​s11128-012-0421-8). In this paper, we adopt the mutual information, the measurement-induced disturbance and the quantum mutual information to measure the classical correlation, the quantum correlation and the total correlation between two particles respectively. Our conclusion is that the correlation between the particles of the two-particle controlled interacting quantum walks is similar to that of the two-particle interacting quantum walks. It is superb for keeping the quantum Hash scheme safe.

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Literature
2.
go back to reference Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)ADSCrossRef Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)ADSCrossRef
3.
go back to reference Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011)ADSCrossRef Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011)ADSCrossRef
5.
go back to reference \(\text{ G}\ddot{o}\text{ n}\ddot{u}\)lol, M., Aydiner, E., Shikano, Y., \(\text{ M}\ddot{u}\)stecaplio\(\tilde{g}\)lu, \(\ddot{O}\).E.,: Survival probability in a one-dimensional quantum walk on a trapped lattice. New J. Phys. 13, 033037 (2011) \(\text{ G}\ddot{o}\text{ n}\ddot{u}\)lol, M., Aydiner, E., Shikano, Y., \(\text{ M}\ddot{u}\)stecaplio\(\tilde{g}\)lu, \(\ddot{O}\).E.,: Survival probability in a one-dimensional quantum walk on a trapped lattice. New J. Phys. 13, 033037 (2011)
6.
go back to reference Franco, C.D., Gettrick, M.M., Busch, Th: Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. Phys. Rev. Lett. 106, 080502 (2011)CrossRef Franco, C.D., Gettrick, M.M., Busch, Th: Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. Phys. Rev. Lett. 106, 080502 (2011)CrossRef
7.
go back to reference Franco, C.D., Gettrick, M.M., Machida, T., Busch, Th: Alternate two-dimensional quantum walk with a single-qubit coin. Phys. Rev. A 84, 042337 (2011)ADSCrossRef Franco, C.D., Gettrick, M.M., Machida, T., Busch, Th: Alternate two-dimensional quantum walk with a single-qubit coin. Phys. Rev. A 84, 042337 (2011)ADSCrossRef
8.
go back to reference \(\check{S}\text{ tefa}\check{n}\acute{a}\)k, M., Barnett, S.M., Koll\(\acute{a}\)r, B., Kiss, T., Jex, I.: Directional correlations in quantum walks with two particles. New J. Phys. 13, 033029 (2011) \(\check{S}\text{ tefa}\check{n}\acute{a}\)k, M., Barnett, S.M., Koll\(\acute{a}\)r, B., Kiss, T., Jex, I.: Directional correlations in quantum walks with two particles. New J. Phys. 13, 033029 (2011)
9.
go back to reference Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85, 022307 (2012)ADSCrossRef Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85, 022307 (2012)ADSCrossRef
10.
go back to reference Omar, Y.: Paunkovi\(\acute{c}\), N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006) Omar, Y.: Paunkovi\(\acute{c}\), N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)
11.
go back to reference Pathak, P.K., Agarwal, G.S.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)MathSciNetADSCrossRef Pathak, P.K., Agarwal, G.S.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)MathSciNetADSCrossRef
12.
go back to reference Banuls, M.C., Navarrete, C.: P\(\acute{e}\)rez, A., Rold\(\acute{a}\)n, E., Soriano, J.C.: Quantum walk with a time-dependent coin. Phys. Rev. A 73, 062304 (2006) Banuls, M.C., Navarrete, C.: P\(\acute{e}\)rez, A., Rold\(\acute{a}\)n, E., Soriano, J.C.: Quantum walk with a time-dependent coin. Phys. Rev. A 73, 062304 (2006)
13.
go back to reference Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRef Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRef
14.
15.
16.
go back to reference Rao, B.R., Srikanth, R., Chandrashekar, C.M., Banerjee, S.: Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord. Phys. Rev. A 83, 064302 (2011)ADSCrossRef Rao, B.R., Srikanth, R., Chandrashekar, C.M., Banerjee, S.: Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord. Phys. Rev. A 83, 064302 (2011)ADSCrossRef
17.
go back to reference Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011)ADSCrossRef Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011)ADSCrossRef
18.
go back to reference Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRef Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRef
19.
go back to reference Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)ADSCrossRef Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)ADSCrossRef
20.
go back to reference Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)MathSciNetADSCrossRef Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)MathSciNetADSCrossRef
21.
go back to reference Li, N., Luo, S.: Total versus quantum correlations in quantum states. Phys. Rev. A 76, 032327 (2007)ADSCrossRef Li, N., Luo, S.: Total versus quantum correlations in quantum states. Phys. Rev. A 76, 032327 (2007)ADSCrossRef
22.
go back to reference Srikanth, R., Banerjee, S., Chandrashekar, C.M.: Quantumness in a decoherent quantum walk using measurement-induced disturbance. Phys. Rev. A 81, 062123 (2010)ADSCrossRef Srikanth, R., Banerjee, S., Chandrashekar, C.M.: Quantumness in a decoherent quantum walk using measurement-induced disturbance. Phys. Rev. A 81, 062123 (2010)ADSCrossRef
Metadata
Title
Analysis of the two-particle controlled interacting quantum walks
Authors
Dan Li
Jie Zhang
Xiu-Wen Ma
Wei-Wei Zhang
Qiao-Yan Wen
Publication date
01-06-2013
Publisher
Springer US
Published in
Quantum Information Processing / Issue 6/2013
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-012-0516-2

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