×

Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states. (English) Zbl 1327.81029

Summary: We present a scheme for bidirectional controlled implementation of arbitrary single qubit operations by using two EPR states and a five-qubit cluster state as the quantum channel. Alice can implement an unknown single-qubit unitary operation on the remote Bob’s quantum system and at the same time, Bob can also remotely implement an arbitrary single-qubit unitary operation on Alice’s quantum system if they cooperate with the controller. We also study the bidirectional controlled implementation of unitary operations belonging to the restricted sets. It is shown that receivers can prepare the target state by performing corresponding unitary operations on their entangled particles if they cooperate with the controller.

MSC:

81P15 Quantum measurement theory, state operations, state preparations
81P40 Quantum coherence, entanglement, quantum correlations
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bennett, CH; Wiesner, SJ, No article title, Phys. Rev. Lett., 69, 2881 (1992) · Zbl 0968.81506 · doi:10.1103/PhysRevLett.69.2881
[2] Liu, XS; Long, GL; Tong, DM; Li, F., No article title, Phys. Rev. A, 65, 022304 (2002) · doi:10.1103/PhysRevA.65.022304
[3] Bennett, C.H., Brassad, G.: Proceedings IEEE International Conference on Computers, Systems and Signal Processing Bangalore, India. IEEE, New York, p. 175 (1984)
[4] Long, GL; Liu, XS, No article title, Phys. Rev. A, 65, 032302 (2002) · doi:10.1103/PhysRevA.65.032302
[5] Deng, FG; Long, GL, No article title, Phys. Rev. A, 68, 042315 (2003) · doi:10.1103/PhysRevA.68.042315
[6] Li, XH; Deng, FG; Zhou, HY, No article title, Phys. Rev. A, 78, 022321 (2008) · doi:10.1103/PhysRevA.78.022321
[7] Li, CY; Li, YS, No article title, Chin. Phys. Lett., 28, 120306 (2011) · doi:10.1088/0256-307X/28/12/120306
[8] Bennett, CH; Brassard, G.; Crepeau, C.; Jozsa, R.; Peres, A.; Wootters, WK, No article title, Phys. Rev. Lett., 70, 1895 (1993) · Zbl 1051.81505 · doi:10.1103/PhysRevLett.70.1895
[9] Yan, FL; Yang, LG, No article title, Nuovo Cimento B, 118, 79 (2003)
[10] Yan, FL; Ding, HW, No article title, Chin. Phys. Lett., 23, 17 (2006) · doi:10.1088/0256-307X/23/1/006
[11] Karlsson, A.; Bourennane, M., No article title, Phys. Rev. A, 58, 4394 (1998) · doi:10.1103/PhysRevA.58.4394
[12] Deng, FG; Li, CY; Li, YS; Zhou, HY; Wang, Y., No article title, Phys. Rev. A, 72, 022338 (2005) · doi:10.1103/PhysRevA.72.022338
[13] Deng, FG; Li, XH; Li, CY; Zhou, P.; Zhou, HY, No article title, Phys. Rev. A, 72, 044301 (2005) · doi:10.1103/PhysRevA.72.044301
[14] Zhou, P.; Li, XH; Deng, FG; Zhou, HY, No article title, J. Phys. A, 420, 13121 (2007) · Zbl 1124.81011 · doi:10.1088/1751-8113/40/43/019
[15] Long, LR; Li, HW; Zhou, P.; Fan, C.; Yin, CL, No article title, Mech. Astron., 54, 484 (2011) · doi:10.1007/s11433-011-4246-8
[16] Li, Z.; Long, LR; Zhou, P.; Yin, CL, No article title, Sci. China-Phys. Mech. Astron., 55, 2445 (2012) · doi:10.1007/s11433-012-4947-7
[17] Bennett, CH; Brassard, G.; Popescu, S.; Schumacher, B.; Smolin, JA; Wootters, WK, No article title, Phys. Rev. Lett., 76, 722 (1996) · doi:10.1103/PhysRevLett.76.722
[18] Deutsch, D.; Ekert, A.; Jozsa, R.; Macchiavello, C.; Popescu, S.; Sanpera, A., No article title, Phys. Rev. Lett., 77, 2818 (1996) · doi:10.1103/PhysRevLett.77.2818
[19] Sheng, YB; Deng, FG; Zhou, HY, No article title, Phys. Rev. A, 77, 042308 (2008) · doi:10.1103/PhysRevA.77.042308
[20] Sheng, YB; Deng, FG, No article title, Phys. Rev. A, 81, 032307 (2010) · doi:10.1103/PhysRevA.81.032307
[21] Sheng, YB; Deng, FG, No article title, Phys. Rev. A, 82, 044305 (2010) · doi:10.1103/PhysRevA.82.044305
[22] Sheng, YB; Zhou, L.; Zhao, SM; Zheng, BY, No article title, Phys. Rev. A, 85, 012307 (2012) · doi:10.1103/PhysRevA.85.012307
[23] Sheng, YB; Zhou, L.; Zhao, SM, No article title, Phys. Rev. A, 85, 042302 (2012) · doi:10.1103/PhysRevA.85.042302
[24] Ren, BC; Deng, FG, No article title, Laser. Phys. Lett., 10, 115201 (2013) · doi:10.1088/1612-2011/10/11/115201
[25] Wang, C.; Zhang, Y.; Jin, GS, No article title, Quantum Inf. Comput., 11, 988 (2011) · Zbl 1238.81040
[26] Wang, C.; Zhang, Y.; Jin, GS, No article title, Phys. Rev. A, 84, 032307 (2011) · doi:10.1103/PhysRevA.84.032307
[27] Ren, BC; Du, FF; Deng, FG, No article title, Phys. Rev. A, 88, 012302 (2013) · doi:10.1103/PhysRevA.88.012302
[28] Wang, TJ; Song, SY; Long, GL, No article title, Phys. Rev. A, 85, 062311 (2012) · doi:10.1103/PhysRevA.85.062311
[29] Sheng, YB; Zhou, L.; Long, GL, No article title, Phys. Rev. A, 88, 022302 (2013) · doi:10.1103/PhysRevA.88.022302
[30] Sheng, YB; Zhou, L., No article title, Entropy, 15, 1776 (2013) · Zbl 1297.81039 · doi:10.3390/e15051776
[31] Shor, P.W.: Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, p.124 (1994)
[32] Feng, GR; Xu, GF; Long, GL, No article title, Phys. Rev. Lett., 110, 190501 (2013) · doi:10.1103/PhysRevLett.110.190501
[33] Ren, BC; Wei, HR; Deng, FG, No article title, Laser. Phys. Lett., 10, 095202 (2013) · doi:10.1088/1612-2011/10/9/095202
[34] Ren, BC; Deng, FG, No article title, Sci. Rep., 4, 4623 (2014)
[35] Li, CY; Zhang, ZR; Sun, SH; Jiang, MS; Liang, LM, No article title, J. Opt. Soc. Am. B, 30, 1872 (2013) · doi:10.1364/JOSAB.30.001872
[36] Wei, HR; Deng, FG, No article title, Opt. Express, 21, 17671 (2013) · doi:10.1364/OE.21.017671
[37] Wei, HR; Deng, FG, No article title, Phys. Rev. A, 87, 022305 (2013) · doi:10.1103/PhysRevA.87.022305
[38] Shi, X.; Wei, LF; OH, CH, No article title, Sci. China-Phys. Mech. Astron., 57, 1718 (2014) · doi:10.1007/s11433-014-5547-5
[39] Long, Y.; Feng, GR; Pearson, J.; Long, GL, No article title, Sci. China-Phys. Mech. Astron, 57, 1256 (2014) · doi:10.1007/s11433-014-5494-1
[40] Sun, RH; Ye, MY; Lin, XM, No article title, Sci. China-Phys. Mech. Astron., 56, 1755 (2013) · doi:10.1007/s11433-013-5177-3
[41] Pati, AK, No article title, Phys. Rev. A, 63, 014302 (2001) · doi:10.1103/PhysRevA.63.014302
[42] Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Phys. Rev. Lett. 87, 077902 (2001)
[43] Lo, HK, No article title, Phys. Rev. A, 62, 012313 (2000) · doi:10.1103/PhysRevA.62.012313
[44] Ai, LT; Nong, L.; Zhou, P., No article title, Int. J. Theor. Phys., 53, 159 (2014) · Zbl 1284.81025 · doi:10.1007/s10773-013-1793-y
[45] Long, LR; Zhou, P.; Li, Z.; Yin, CL, No article title, Int. J. Theor. Phys., 51, 2438 (2012) · Zbl 1252.81026 · doi:10.1007/s10773-012-1124-8
[46] Zhou, NR; Cheng, HL; Tao, XY; Gong, LH, No article title, Quantum Inf. Process., 13, 513 (2014) · Zbl 1291.81035 · doi:10.1007/s11128-013-0667-9
[47] Liao, YM; Zhou, P.; Qin, XC; He, YH, No article title, Quantum Inf. Process, 13, 615 (2014) · Zbl 1293.81013 · doi:10.1007/s11128-013-0677-7
[48] Huelga, SF; Vaccaro, JA; Chefles, A., No article title, Phys. Rev. A, 63, 042303 (2001) · Zbl 1255.81109 · doi:10.1103/PhysRevA.63.042303
[49] Huelga, SF; Plenio, MB; Vaccaro, JA, No article title, Phys. Rev. A, 65, 042316 (2002) · doi:10.1103/PhysRevA.65.042316
[50] Zhang, YS; Ye, MY; Guo, GC, No article title, Phys. Rev. A, 71, 062331 (2005) · doi:10.1103/PhysRevA.71.062331
[51] Cirac, JI; Ekert, AK; Huelga, SF; Macchiavello, C., No article title, Phys. Rev. A, 59, 4249 (1999) · doi:10.1103/PhysRevA.59.4249
[52] Eisert, J.; Jacobs, K.; Papadopoulos, P.; Plenio, MB, No article title, Phys. Rev. A, 62, 052317 (2000) · doi:10.1103/PhysRevA.62.052317
[53] Xiang, GY; Li, J.; Guo, GC, No article title, Phys. Rev. A, 71, 044304 (2005) · doi:10.1103/PhysRevA.71.044304
[54] Huelga, SF; Plenio, MB; Xiang, GY; Li, J.; Guo, GC, No article title, J. Opt. B, 7, s384 (2005) · doi:10.1088/1464-4266/7/10/026
[55] Wang, AM, No article title, Phys. Rev. A, 74, 032317 (2006) · doi:10.1103/PhysRevA.74.032317
[56] Zhao, NB; Wang, AM, No article title, Phys. Rev. A, 78, 014305 (2008) · Zbl 1255.81121 · doi:10.1103/PhysRevA.78.014305
[57] Liang, Q.; Wang, AM, No article title, Commun. Theor. Phys., 50, 1233 (2008) · Zbl 1392.81092 · doi:10.1088/0253-6102/50/5/44
[58] Wang, AM, No article title, Phys. Rev. A, 75, 062323 (2007) · doi:10.1103/PhysRevA.75.062323
[59] Fan, QB; Liu, DD, No article title, Sci. China Ser. G-Phys. Mech. Astron, 51, 1661 (2008) · doi:10.1007/s11433-008-0163-x
[60] Chen, LB; Liu, YH; Lu, H., No article title, Mod, Phys. Lett. B, 24, 431 (2010) · Zbl 1187.81048 · doi:10.1142/S0217984910022500
[61] Zhan, YB; Li, XW; Ma, PC; Shi, J., No article title, Chin. Phys. B, 22, 040306 (2013) · doi:10.1088/1674-1056/22/4/040306
[62] Chen, LB; Jin, RB; Peng, T.; Lu, H., No article title, Int. J. Mod. Phys. B, 25, 2853 (2011) · Zbl 1333.81069 · doi:10.1142/S0217979211101041
[63] Zhang, ZJ; Cheung, CY, No article title, J. Phys. B, 44, 165508 (2011) · doi:10.1088/0953-4075/44/16/165508
[64] Ye, BL; Liu, YM; Liu, XS; Zhan, ZJ, No article title, Chin. Phys. Lett., 30, 020301 (2013) · doi:10.1088/0256-307X/30/2/020301
[65] Wang, SF; Liu, YM; Chen, JL; Liu, XS; Zhan, ZJ, No article title, Quantum Inf. Process., 12, 2497 (2013) · Zbl 1270.81050 · doi:10.1007/s11128-013-0537-5
[66] Liu, DC; Liu, YM; Yin, XF; Liu, XS; Zhan, ZJ, No article title, Int. J. Quantum Inform., 11, 1350011 (2013) · Zbl 1268.81036 · doi:10.1142/S0219749913500111
[67] Ji, QB; Liu, YM; Liu, XS; Yin, XF; Zhan, ZJ, No article title, Commun. Theor. Phys., 165, 60 (2013)
[68] Ji, QB; Liu, YM; Xie, CM; Yin, XF; Zhan, ZJ, No article title, Quantum Inf. Process, 13, 1659 (2014) · Zbl 1306.81018 · doi:10.1007/s11128-014-0759-1
[69] Xing, H.; Liu, YM; Xie, CM; Ji, QB; Zhan, ZJ, No article title, Quantum Inf. Process., 13, 1553 (2014) · Zbl 1303.81043 · doi:10.1007/s11128-014-0750-x
[70] Xing, H.; Liu, YM; Yin, XF; Liu, XS; Zhan, ZJ, No article title, Quantum Inf. Process., 12, 2453 (2013) · Zbl 1270.81043 · doi:10.1007/s11128-013-0533-9
[71] Deng, FG; Long, GL, No article title, Phys. Rev. A, 70, 012311 (2004) · doi:10.1103/PhysRevA.70.012311
[72] Gu, B.; Huang, YG; Fang, x.; Chen, YL, No article title, Commun. Theor. Phys., 56, 659 (2011) · Zbl 1247.81094 · doi:10.1088/0253-6102/56/4/11
[73] Zha, XW; Zou, ZC; Qi, JX; Song, HY, No article title, Int. J. Theor. Phys., 52, 1740 (2013) · doi:10.1007/s10773-012-1208-5
[74] Li, YH; Nie, LP, No article title, Int. J. Theor. Phys., 52, 1630 (2013) · doi:10.1007/s10773-013-1484-8
[75] Li, YH; Li, XL; Sang, MH; Nie, YY; Wang, ZS, No article title, Quantum Inf. Process., 12, 3835 (2013) · Zbl 1303.81061 · doi:10.1007/s11128-013-0638-1
[76] Yan, A., No article title, Int. J. Theor. Phys., 52, 3870 (2013) · Zbl 1282.81044 · doi:10.1007/s10773-013-1694-0
[77] Shukla, C.; Banerjee, A.; Pathak, A., No article title, Int. J. Theor. Phys., 52, 3790 (2013) · doi:10.1007/s10773-013-1684-2
[78] Chen, YT; Hwang, T., No article title, Quantum Inf. Process, 12, 3545 (2013) · Zbl 1283.81079 · doi:10.1007/s11128-013-0618-5
[79] Chang, Y.; Xu, CX; Zhang, SB; Yan, LL, No article title, Chinese Sci. Bull., 59, 2541 (2014) · doi:10.1007/s11434-014-0339-x
[80] Li, XH; Deng, FG; Zhou, HY, No article title, Appl. Phys. Lett., 91, 144101 (2007) · doi:10.1063/1.2794433
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.