Deterministic hierarchical quantum operation sharing with five-qubit partially entangled states. (English) Zbl 1542.81168
Summary: To study quantum remote control in the form of hierarchical quantum sharing, by using a Hadamard gate, control-NOT gates and rotation gates, we construct a five-qubit partially entangled state as quantum channels of quantum remote control. By integrating the ideas of hierarchical quantum state sharing and quantum operation teleportation, we put forward two novel schemes for quadripartite hierarchical sharing a single-qubit quantum operation on a qubit in any sharer’s site with the help of the local operations and classical communication. In each scheme, there is a hierarchy among the receivers concerning powers to reconstruct the conceivable state. Owing to various unitary operations and projective measurements, the unit success probability can always be achieved irrespective of the parameters of the pre-shared partially entangled state as quantum channel. The first scheme is applicable for arbitrary unitary operations, while the other one is valid only if the operation \(\mathcal{U}_d\) (\(d = 0, 1\)) in question is known to belongs to some restricted sets. Consequently, the latter scheme is more economical in terms of quantum and classical resources, and the local operation complexity involved is also reduced.
MSC:
| 81P48 | LOCC, teleportation, dense coding, remote state operations, distillation |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81Q93 | Quantum control |
Keywords:
quantum operation sharing; hierarchical quantum communication; partially entangled state; single-qubit unitary operationReferences:
| [1] | Bennet, CH; Brassard, G.; Crépeau, C.; Jozsa, R.; Pere, A.; Wootters, WK, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett., 70, 1895-1899 (1993) · Zbl 1051.81505 · doi:10.1103/PhysRevLett.70.1895 |
| [2] | Bouwmeeter, D.; Mattle, K.; Pan, JW; Weinfurter, H.; Zeilinger, A.; Zukowski, M., Experimental quantum teleportation of arbitrary quantum state, Appl. Phys. B Lassers Opt., 67, 6, 749-752 (1998) · doi:10.1007/s003400050575 |
| [3] | Roy, S.; Ghosh, B., A revisit to non-maximally entangled mixed states: teleportation witness, noisy channel and discord, Quantum Inf. Process., 16, 4, 108 (2017) · Zbl 1373.81081 · doi:10.1007/s11128-017-1557-3 |
| [4] | Wen, K.; Zhao, Y.; Tu, J.; Xu, J.; Li, Y., A coherent receiver based on SIM for quantum communication, IEEE Photon. Technol. Lett., 30, 1, 27-31 (2018) · doi:10.1109/LPT.2017.2771957 |
| [5] | Jiang, LN, Quantum teleportation under different collective noise environment, Int. J. Theor. Phys., 58, 2, 522-530 (2019) · Zbl 1416.81040 · doi:10.1007/s10773-018-3951-8 |
| [6] | Joy, D.; Sabir, M., Efficient schemes for the quantum teleportation of a sub-class of tripartite entangled states, Quantum Inf. Process., 17, 7, 170 (2018) · Zbl 1448.81194 · doi:10.1007/s11128-018-1937-3 |
| [7] | Cheung, CY; Zhang, ZJ, Criterion for faithful teleportation with an arbitrary multiparticle channel, Phys. Rev. A, 80 (2009) · doi:10.1103/PhysRevA.80.022327 |
| [8] | Ursin, R.; Jennewein, T.; Aspelmeyer, M., Communication: quantum teleportation across the Danuble, Nature, 430, 849 (2004) · doi:10.1038/430849a |
| [9] | Barrett, MD; Chiaverini, J.; Schaetz, T., Deteministic quantum teleportation of atomic qubits, Nature, 429, 737-739 (2004) · doi:10.1038/nature02608 |
| [10] | Marcikic, I.; De Riedmatten, H.; Tittel, W., Long-distance teleportation of qubits at telecommunication wavelengths, Nature, 421, 509-513 (2003) · doi:10.1038/nature01376 |
| [11] | Jin, XM; Ren, JG; Yang, B., Experimental free-space quantum teleportation, Nat. Photonics, 4, 376-381 (2010) · doi:10.1038/nphoton.2010.87 |
| [12] | Sang, MH; Dai, HL, Controlled teleportation of an arbitrary three-qubit state by using two four-qubit entangled states, Int. J. Theor. Phys., 53, 6, 1930-1934 (2014) · Zbl 1298.81041 · doi:10.1007/s10773-014-1997-9 |
| [13] | Li, DF; Wang, R.; Zhang, J., A noise immunity controlled quantum teleportation protocal, Quantum Inf. Process., 15, 11, 4819-4837 (2016) · Zbl 1357.81048 · doi:10.1007/s11128-016-1416-7 |
| [14] | Hou, K.; Bao, DQ; Zhu, CJ; Yang, YP, Controlled teleportation of an arbitrary two-qubit entanglement in noises environment, Quantum Inf. Process., 18, 104 (2019) · Zbl 1417.81061 · doi:10.1007/s11128-019-2218-5 |
| [15] | Chen, X.; Jiang, M.; Chen, XP; Li, H., Quantum state sharing of an arbitrary three-qubit state by using three sets of W-class states, Quantum Inf. Process., 12, 2405 (2013) · Zbl 1270.81068 · doi:10.1007/s11128-013-0532-x |
| [16] | Peng, JY; Mo, ZW, Quantum sharing an unknown multi-particle state via POVM, Int. J. Theor. Phys., 52, 2, 620-633 (2013) · Zbl 1264.81090 · doi:10.1007/s10773-012-1369-2 |
| [17] | Muralidharan, S.; Jain, S.; Panigrahi, PK, Splitting of quantum information using N-qubit linear cluster states, Opt. Commun., 284, 1082 (2011) · doi:10.1016/j.optcom.2010.10.026 |
| [18] | Peng, JY; Bai, MQ; Mo, ZW, Hierarchical and probabilistic quantum state sharing via a non- maximally entangled \(|\chi \rangle\) state, Chin. Phys. B, 23 (2014) · doi:10.1088/1674-1056/23/1/010304 |
| [19] | Zhang, ZJ; Li, Y.; Man, ZX, Multiparty quantum secret sharing, Phys. Rev. A, 71 (2005) · Zbl 1227.81151 · doi:10.1103/PhysRevA.71.044301 |
| [20] | Zhou, RG; Xu, R.; Lan, H., Bidirectional quantum quantum teleportation by using six-qubit cluster state, IEEE Access, 7, 44269-44275 (2019) · doi:10.1109/ACCESS.2019.2901960 |
| [21] | Ma, PC; Chen, GB; Li, XW; Zhan, YB, Bidirectional controlled quantum teleportation in the three-dimension system, Int. J. Theor. Phys., 57, 7, 2233-2240 (2018) · Zbl 1394.81060 · doi:10.1007/s10773-018-3748-9 |
| [22] | Peng, JY; Bai, MQ; Mo, ZW, Bidirectional quantum states sharing, Int. J. Theor. Phys., 55, 2481-2489 (2016) · Zbl 1338.81105 · doi:10.1007/s10773-015-2885-7 |
| [23] | Wu, F.; Bai, MQ; Zhang, YC, Cyclic quantum teleportation of an unknown multi-particle high-dimension state, Mod. Phys. Lett. B, 34, 5, 2050073 (2020) · doi:10.1142/S0217984920500736 |
| [24] | Peng, JY; He, Y., Annular controlled teleportation, Int. J. Theor. Phys., 58, 3271-3281 (2019) · Zbl 1428.81047 · doi:10.1007/s10773-019-04202-8 |
| [25] | Zhou, RG; Ling, C., Asymmetric cyclic controlled quantum teleportation by using nine-qubit entangled state, Int. J. Theor. Phys., 60, 3435-3459 (2021) · Zbl 1528.81080 · doi:10.1007/s10773-021-04825-w |
| [26] | Peng, J.Y., Tang, L., Yang, Z., et al.: Cyclic teleportation in noisy channel with nondemolition parity analysis and weak measurement. Quantum Inf. Process, pp. 21-114 (2022) · Zbl 1508.81379 |
| [27] | Shukla, C.; Pathak, A., Hierarchical quantum communication, Phys. Lett., 377, 19-20, 1337-1344 (2013) · Zbl 1292.81019 · doi:10.1016/j.physleta.2013.04.010 |
| [28] | Peng, JY; Wo, ZW, Hierarchical and probabilistic quantum state sharing with a nonmaximally four-qubit cluster state, Int. J. Quantum. Inf., 11, 1350004 (2013) · Zbl 1267.81099 · doi:10.1142/S0219749913500044 |
| [29] | Huelga, SF; Vanccaro, JA; Chefles, A., Quantum remote control: teleportation of unitary operations, Phys. Rev. A, 63 (2001) · Zbl 1255.81109 · doi:10.1103/PhysRevA.63.042303 |
| [30] | Zou, XB; Pahlke, K.; Mathis, W., Teleportation implementation of nondeterministic quantum logic operations by using linear optical elements, Phys. Rev. A, 65 (2002) · doi:10.1103/PhysRevA.65.064305 |
| [31] | Wang, AM, Combined and controlled remote implementations of partially unknown quantum operations of multiqubits using Greenberger-Horne-Zeilinger states, Phys. Rev. A, 75 (2007) · doi:10.1103/PhysRevA.75.062323 |
| [32] | Peng, JY; He, Y., Cyclic controlled remote implementation of partially unknown quantum operations, Int. J. Theor. Phys., 58, 3065-3072 (2019) · Zbl 1422.81059 · doi:10.1007/s10773-019-04185-6 |
| [33] | Zhao, NB; Wang, AM, Hybrid protocol of remote implementations of quantum operations, Phys. Rev. A, 76 (2007) · doi:10.1103/PhysRevA.76.062317 |
| [34] | Peng, JY; Lei, HX, Cyclic remote implementation of partially unknown quantum operations, Chin. J. Electron., 30, 2, 378-383 (2021) · doi:10.1049/cje.2021.02.010 |
| [35] | Zhang, ZJ; Cheung, CY, Shared quantum remote control: quantum operation sharing, J. Phys. B: At. Mol. Opt. Phys., 44, 16 (2011) · doi:10.1088/0953-4075/44/16/165508 |
| [36] | Zhang, KJ; Zhang, L.; Song, TT; Yang, YH, A potential application in quantum networks- deterministic quantum operation sharing schemes with Bell ststes, Sci. China-Phys. Mech. Astron., 59 (2016) · doi:10.1007/s11433-016-0021-5 |
| [37] | Peng, JY; Xiang, Y., Multiparty quantum rotation operation sharing, Int. J. Theor. Phys., 60, 3771-3780 (2021) · Zbl 1483.81035 · doi:10.1007/s10773-021-04942-6 |
| [38] | Xing, H.; Liu, DC; Xing, PF, Deterministic tripartite sharing of eight restricted sets of single-qubit operations with two Bell states or a GHZ state, Int. J. Quantum Inf., 12, 1450012 (2014) · Zbl 1301.81028 · doi:10.1142/S0219749914500129 |
| [39] | Ji, QB; Liu, YM; Yin, XF, Quantum operation sharing with symmetric and asymmertric W states, Quantum Inf. Process., 12, 2453 (2013) · Zbl 1270.81043 · doi:10.1007/s11128-013-0533-9 |
| [40] | Ye, BL; Liu, YM; Liu, XS; Zhang, ZJ, Remotely sharing a single-qubit operation with a five-qubit genuine state, Chin. Phys. Lett., 30 (2013) · doi:10.1088/0256-307X/30/2/020301 |
| [41] | Yuan, H.; Zhang, WB; Yin, XF, Simplistic quantum operation sharing with five-qubit genuinely entangled state, Quantum Inf. Process., 19, 122 (2020) · Zbl 1508.81347 · doi:10.1007/s11128-020-2620-z |
| [42] | Peng, JY; Bai, MQ; Mo, ZW, Multicharacters remote rotation sharing with five-particle cluster state, Quantum Inf. Process., 18, 339 (2019) · Zbl 1508.81319 · doi:10.1007/s11128-019-2457-5 |
| [43] | Wang, SF; Liu, YM; Chen, JI; Liu, XS; Zhang, ZJ, Deterministic single-qubit operation sharing with five-qubit cluster state, Quantum Inf. Process., 12, 2497 (2013) · Zbl 1270.81050 · doi:10.1007/s11128-013-0537-5 |
| [44] | Xing, H., Four-party deterministic operation sharing with six-qubit cluster state, Quantum Inf. Process., 13, 1553 (2014) · Zbl 1303.81043 · doi:10.1007/s11128-014-0750-x |
| [45] | Peng, J., Tripartite operation sharing with five-qubit Brown state, Quantum Inf. Process., 15, 2465 (2016) · Zbl 1348.81105 · doi:10.1007/s11128-016-1281-4 |
| [46] | Zhou, SQ; Bai, MQ; Zhang, CY, Analysis and construction of four-party deterministic operation sharing with a generalized seven-qubit Brown state, Mod. Phys. Lett. B, 31, 1750190 (2017) · doi:10.1142/S0217984917501901 |
| [47] | Peng, JY; Bai, MQ; Tang, L., Perfect controlled joint remote state preparation of arbitrary multi-qubit states independent of entanglement degree of the quantum channel, Quantum Inf. Process., 20, 10, 1-18 (2021) · Zbl 1509.81021 · doi:10.1007/s11128-021-03282-y |
| [48] | Anu, V.; Shukla, C., An integrated hierarchical dynamic quantum secret sharing protocol, Int. J. Theor. Phys., 54, 3143-3154 (2015) · Zbl 1325.81069 · doi:10.1007/s10773-015-2552-z |
| [49] | Han, LF; Liu, YM; Shi, SH; Zang, ZJ, Improving the security of a quantum secret sharing protocol between multiparty and multiparty without entanglement, Phys. Lett. A, 361, 24 (2007) · Zbl 1175.94110 · doi:10.1016/j.physleta.2006.09.009 |
| [50] | Bouwmeester, D.; Pan, JW; Mattle, K., Experimental quantum teleportation, Nature, 190, 575 (1997) · Zbl 1369.81006 · doi:10.1038/37539 |
| [51] | Solano, E.; Cesar, CL; de Matos Filho, RL; Zagury, N., Reliable teleportation in trapped ions, Eur. Phys. J. D., 13, 121 (2001) · doi:10.1007/s100530170293 |
| [52] | Zheng, SB, Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement, Phys. Rev. A, 69 (2004) · doi:10.1103/PhysRevA.69.064302 |
| [53] | Riebe, M.; Häffner, H.; Roos, CF, Deterministic quantum teleportation with atms, Nature, 429, 734 (2004) · doi:10.1038/nature02570 |
| [54] | Lim, HT; Kim, YS; Ra, YS, Experimental realization of an approximate transpose operation for qutrit systems using a structural physical approximation, Phys. Rev. A, 86 (2012) · doi:10.1103/PhysRevA.86.042334 |
| [55] | Peng, ZH; Zou, J.; Liu, XJ, Scheme for implementing efficient quantum information processing with multiqubit W-class states in equity QED, J. Phys. B: At. Mol. Opt. Phys., 41, 1065505 (2008) · doi:10.1088/0953-4075/41/6/065505 |
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.
