联合噪声信道下基于部分纠缠信道的非定域Toffoli门远程实现
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摘要
量子操控远程实现是量子通信重要任务之一,最近,基于量子纠缠信道的非定域量子门引起了广泛关注.基于不同信道提出了双量子比特控制非门,三量子比特Toffoli门远程实现方案.本文研究信道联合噪声下基于部分纠缠信道的三粒子非定域Toffoli门远程实现方案,提出了两个非最大纠缠信道下可克制信道联合噪声的非定域Toffoli门远程实现方案.一个方案用于联合退相位噪声下基于部分纠缠信道的非定域Toffoli门远程实现,另一个用于联合转动噪声下非定域Toffoli门远程实现.通信方先使用退相干无关子空间克制信道联合噪声影响,再通过引入附加粒子和执行联合幺正演化消除部分纠缠信道对非定域Toffoli门远程实现影响.通讯方仅需使用部分纠缠态来实现非定域量子门,与其他方案相比,具有可行性强的优点.
Remote implementation of nonlocal quantum gates is one of the central tasks in quantum communication. Researchers devote much interest in remote implementation of nonlocal quantum gates via quantum entangled channel. Remote implementation protocols of two-qubit controlled-not gate, three-qubit Toffoli gate have been presented. We present two schemes for remote implementation of nonlocal Toffoli gate via partially entangled quantum channel against collective noise. The first is used to remote implementing of nonlocal Toffoli gate via partially entangled channel against collectivedephasing noise, and the second is used to remote implementing of nonlocal Toffoli gate against collective-rotation noise.The schemes are tolerant of collective-dephasing noise and collective-rotating noise. The agents can implement the Toffoli gate nonlocally with partially entangled quantum channel by introducing an auxiliary qubit and performing general evolution. The schemes are more convenient in application since they only requires partially entangled quantum states for nonlocal implementation of quantum operations.
Remote implementation of nonlocal quantum gates is one of the central tasks in quantum communication. Researchers devote much interest in remote implementation of nonlocal quantum gates via quantum entangled channel. Remote implementation protocols of two-qubit controlled-not gate, three-qubit Toffoli gate have been presented. We present two schemes for remote implementation of nonlocal Toffoli gate via partially entangled quantum channel against collective noise. The first is used to remote implementing of nonlocal Toffoli gate via partially entangled channel against collectivedephasing noise, and the second is used to remote implementing of nonlocal Toffoli gate against collective-rotation noise.The schemes are tolerant of collective-dephasing noise and collective-rotating noise. The agents can implement the Toffoli gate nonlocally with partially entangled quantum channel by introducing an auxiliary qubit and performing general evolution. The schemes are more convenient in application since they only requires partially entangled quantum states for nonlocal implementation of quantum operations.
引文
1 Nielsen M A,Chuang I L.Quantum Computation and Quantum Information.2nd ed.London:Cambridge University Press,2010.26-28
2 Bennett C H,Brassard G,Crepeau C,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.Phys Rev Lett,1993,70:1895-1899
3 Long G L,Liu X S.Theoretically efficient high-capacity quantum-key-distribution scheme.Phys Rev A,2002,65:032302
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7 Deng F G,Long G L.Secure direct communication with a quantum one-time pad.Phys Rev A,2004,69:052319
8 Zheng C,Long G F.Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs.Sci China-Phys Mech Astron,2014,57:1238-1243
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10 Karlsson A,Bourennane M.Quantum teleportation using three-particle entanglement.Phys Rev A,1998,58:4394-4400
11 Bouwmeester D,Pan J W,Mattle K,et al.Experimental quantum teleportation.Nature,1997,390:575-579,arXiv:1901.11004
12 Xiao X,Yao Y,Zhong W J,et al.Enhancing teleportation of quantum Fisher information by partial measurements.Phys Rev A,2016,93:012307,arXiv:1510.07359
13 Zha X W,Zhang C M.Teleportation of on N-particle GHZ state via one three-particle W state(in Chinese).Acta Phys Sin,2008,57:1339-1342[查新未,张淳民.利用一个三粒子W态隐形传送N粒子GHZ态.物理学报,2008,57:1339-1342]
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16 Pati A K.Minimum classical bit for remote preparation and measurement of a qubit.Phys Rev A,2000,63:014302
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21 Li Y,Nie L,Li X,et al.Asymmetric bidirectional controlled teleportation by using six-qubit cluster state.Int J Theor Phys,2016,55:3008-3016
22 Yang Y Q,Zha X W,Yu Y.Asymmetric bidirectional controlled teleportation via seven-qubit cluster state.Int J Theor Phys,2016,55:4197-4204
23 Liang H Q,Liu J M,Feng S S,et al.Effects of noises on joint remote state preparation via a GHZ-class channel.Quantum Inf Process,2015,14:3857-3877
24 Zhou P,Jiao X F,Lv S X.Parallel remote state preparation of arbitrary single-qubit states via linear-optical elements by using hyperentangled Bell states as the quantum channel.Quantum Inf Process,2018,17:298
25 Huelga S F,Vaccaro J A,Chefles A,et al.Quantum remote control:Teleportation of unitary operations.Phys Rev A,2001,63:042303
26 He Y H,Lu Q C,Liao Y M,et al.Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states.Int J Theor Phys,2015,54:1726-1736
27 Fan Q B,Liu D D.Controlled remote implementation of partially unknown quantum operation.Sci China Ser G-Phys Mech Astron,2008,51:1661-1667
28 Lin J Y,He J G,Gao Y C,et al.Controlled remote implementation of an arbitrary single-qubit operation with partially entangled quantum channel.Int J Theor Phys,2017,56:1085-1095
29 Wang S,Liu Y,Chen J,et al.Deterministic single-qubit operation sharing with five-qubit cluster state.Quantum Inf Process,2013,12:2497-2507
30 Peng J.Tripartite operation sharing with five-qubit Brown state.Quantum Inf Process,2016,15:2465-2473
31 Tian D P,Tao Y J,Qin M.Teleportation of an arbitrary two-qudit state based on the non-maximally four-qudit cluster state.Sci China Ser G-Phys Mech Astron,2008,51:1523-1528
32 Lv S X,Zhao Z W,Zhou P.Joint remote control of an arbitrary single-qubit state by using a multiparticle entangled state as the quantum channel.Quantum Inf Process,2018,17:8
33 Barenco A,Bennett C H,Cleve R,et al.Elementary gates for quantum computation.Phys Rev A,1995,52:3457-3467
34 Ye M Y,Zhang Y S,Guo G C.Quantum entanglement and quantum operation(in Chinese).Sci Sin-Phys Mech Astron,2007,37:716-722[叶明勇,张永生,郭光灿.量子纠缠和量子操作.中国科学:物理学力学天文学,2007,37:716-722]
35 Chen L B,Lu H.Conclusive qudit states transformation implemented by remote parters(in Chinese).Sci Sin-Phys Mech Astron,2015,45:120301[陈立冰,路洪.远程协作实现高维量子态间的精确转换.中国科学:物理学力学天文学,2015,45:120301]
36 Chen L B,Lu H.Deterministic and controlled many-to-one and one-to-many remote quantum rotations via partially entangled quantum channels(in Chinese).Sci Sin-Phys Mech Astron,2014,44:1187-1195[陈立冰,路洪.利用部分纠缠的量子信道确定性地实现N→1和1→N的受控量子远程旋转.中国科学:物理学力学天文学,2014,44:1187-1195]
37 Xiang G Y,Li J,Guo G C.Teleporting a rotation on remote photons.Phys Rev A,2005,71:044304
38 Huang Y F,Ren X F,Zhang Y S,et al.Experimental teleportation of a quantum controlled-NOT gate.Phys Rev Lett,2004,93:240501
39 Eisert J,Jacobs K,Papadopoulos P,et al.Optimal local implementation of nonlocal quantum gates.Phys Rev A,2000,62:052317
40 Huelga S F,Plenio M B,Vaccaro J A.Remote control of restricted sets of operations:Teleportation of angles.Phys Rev A,2002,65:042316
41 Chen L B,Lu H.Nonlocal multi-target controlled-controlled gate using Greenberger-Horne-Zeilinger channel and qutrit catalysis.Chin Phys B,2015,24:070307
42 Chen L B,Lu H.Quantum networks for implementing locally and conclusively a nonlocal qudit Toffoli gate:Designing and optimizing(in Chinese).Sci Sin-Phys Mech Astron,2016,46:110301[陈立冰,路洪.确定性地实现非局域高维量子Toffoli门的网络设计与优化.中国科学:物理学力学天文学,2016,46:110301]
43 Chen L B,Lu H.Efficient nonlocal m-control and n-target controlled unitary gate using non-symmetric GHZ states.Int J Theor Phys,2018,57:706-714
44 Chou K S,Blumoff J Z,Wang C S,et al.Deterministic teleportation of a quantum gate between two logical qubits.Nature,2018,561:368-373
45 Bennett C H,Brassard G,Popescu S,et al.Purification of noisy entanglement and faithful teleportation via noisy channels.Phys Rev Lett,1996,76:722-725
46 Sheng Y B,Deng F G.Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement.Phys Rev A,2010,81:032307,arXiv:0912.0079
47 Sheng Y B,Deng F G.One-step deterministic polarization-entanglement purification using spatial entanglement.Phys Rev A,2010,82:044305,arXiv:1008.3509
48 Li X H,Deng F G,Zhou H Y.Faithful qubit transmission against collective noise without ancillary qubits.Appl Phys Lett,2007,91:144101,arXiv:0708.0068
49 Walton Z D,Abouraddy A F,Sergienko A V,et al.Decoherence-free subspaces in quantum key distribution.Phys Rev Lett,2003,91:087901
50 Deng F G,Li X H,Li T.Quantum error rejection and fault tolerant quantum communication(in Chinese).Acta Phys Sin,2018,67:130301[邓富国,李熙涵,李涛.基于光量子态避错及容错传输的量子通信.物理学报,2018,67:130301]
51 Yamamoto T,Shimamura J,?zdemir S K,et al.Faithful qubit distribution assisted by one additional qubit against collective noise.Phys Rev Lett,2005,95:040503
52 Li X H,Deng F G,Zhou H Y.Efficient quantum key distribution over a collective noise channel.Phys Rev A,2008,78:022321,arXiv:0808.0042
53 Dong L,Xiu X M,Gao Y J.Three-party controlled quantum teleportation with six-photon entangled states via collective noise channel.Acta Phys Pol B,2010,41:2377-2385
54 Gu B,Pei S X,Song B,et al.Secure quantum communication under joint noise(in Chinese).Sci Sin-Phys Mech Astron,2010,40:177-182[顾斌,裴世鑫,宋标,等.联合噪声下确定的安全量子通信.中国科学:物理学力学天文学,2010,40:177-182]
55 Li Z,Long L R,Zhou P,et al.Probabilistic multiparty-controlled teleportation of an arbitrary m-qubit state with a pure entangled quantum channel against collective noise.Sci China-Phys Mech Astron,2012,55:2445-2451
56 Zhou P,Li H W,Long L R.Probabilistic multiparty joint remote preparation of an arbitrary m-qubit state with a pure entangled channel against collective noise.Int J Theor Phys,2013,52:849-861
57 Takeuchi Y,Fujii K,Ikuta R,et al.Blind quantum computation over a collective-noise channel.Phys Rev A,2016,93:052307,arXiv:1505.04248
58 Sheng Y B,Zhou L.Blind quantum computation with a noise channel.Phys Rev A,2018,98:052343
59 Wang H F,Zhu A D,Zhang S,et al.Optically controlled phase gate and teleportation of a controlled-not gate for spin qubits in a quantum-dotmicrocavity coupled system.Phys Rev A,2013,87:062337,arXiv:1306.4737
60 Hu S,Cui W X,Wang D Y,et al.Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities.Sci Rep,2015,5:11321
61 Chen L B,Lu H.Implementing a nonlocal Toffoli gate using partially entangled qubit pairs.Int J Theor Phys,2011,50:3442-3450
62 Zhou P,Li X H,Deng F G,et al.Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel.J Phys A-Math Theor,2007,40:13121-13130
63 Bourennane M,Eibl M,Gaertner S,et al.Decoherence-free quantum information processing with four-photon entangled states.Phys Rev Lett,2004,92:107901
64 Tsai C L,Hwang T.Semi-quantum key distribution robust against combined collective noise.Int J Theor Phys,2018,57:3410-3418
2 Bennett C H,Brassard G,Crepeau C,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.Phys Rev Lett,1993,70:1895-1899
3 Long G L,Liu X S.Theoretically efficient high-capacity quantum-key-distribution scheme.Phys Rev A,2002,65:032302
4 Zhang W,Ding D S,Sheng Y B,et al.Quantum secure direct communication with quantum memory.Phys Rev Lett,2017,118:220501,arXiv:1609.09184
5 Zhu F,Zhang W,Sheng Y,et al.Experimental long-distance quantum secure direct communication.Sci Bull,2017,62:1519-1524
6 Deng F G,Long G L,Liu X S.Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block.Phys Rev A,2003,68:042317
7 Deng F G,Long G L.Secure direct communication with a quantum one-time pad.Phys Rev A,2004,69:052319
8 Zheng C,Long G F.Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs.Sci China-Phys Mech Astron,2014,57:1238-1243
9 Hu J Y,Yu B,Jing M Y,et al.Experimental quantum secure direct communication with single photons.Light Sci Appl,2016,5:e16144,arXiv:1503.00451
10 Karlsson A,Bourennane M.Quantum teleportation using three-particle entanglement.Phys Rev A,1998,58:4394-4400
11 Bouwmeester D,Pan J W,Mattle K,et al.Experimental quantum teleportation.Nature,1997,390:575-579,arXiv:1901.11004
12 Xiao X,Yao Y,Zhong W J,et al.Enhancing teleportation of quantum Fisher information by partial measurements.Phys Rev A,2016,93:012307,arXiv:1510.07359
13 Zha X W,Zhang C M.Teleportation of on N-particle GHZ state via one three-particle W state(in Chinese).Acta Phys Sin,2008,57:1339-1342[查新未,张淳民.利用一个三粒子W态隐形传送N粒子GHZ态.物理学报,2008,57:1339-1342]
14 Yan L,Ma H Y,Zheng C,et al.Quantum communication scheme based on quantum teleportation(in Chinese).Acta Phys Sin,2017,66:230303[杨璐,马鸿洋,郑超,等.基于量子隐形传态的量子保密通信方案.物理学报,2017,66:230303]
15 Deng F G,Li C Y,Li Y S,et al.Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement.Phys Rev A,2005,72:022338
16 Pati A K.Minimum classical bit for remote preparation and measurement of a qubit.Phys Rev A,2000,63:014302
17 Lo H K.Classical-communication cost in distributed quantum-information processing:A generalization of quantum-communication complexity.Phys Rev A,2000,62:012313
18 Bennett C H,DiVincenzo D P,Shor P W,et al.Remote state preparation.Phys Rev Lett,2001,87:077902
19 Xia Y,Song J,Song H S.Multiparty remote state preparation.J Phys B-At Mol Opt Phys,2007,40:3719-3724
20 Yan A.Bidirectional controlled teleportation via six-qubit cluster state.Int J Theor Phys,2013,52:3870-3873
21 Li Y,Nie L,Li X,et al.Asymmetric bidirectional controlled teleportation by using six-qubit cluster state.Int J Theor Phys,2016,55:3008-3016
22 Yang Y Q,Zha X W,Yu Y.Asymmetric bidirectional controlled teleportation via seven-qubit cluster state.Int J Theor Phys,2016,55:4197-4204
23 Liang H Q,Liu J M,Feng S S,et al.Effects of noises on joint remote state preparation via a GHZ-class channel.Quantum Inf Process,2015,14:3857-3877
24 Zhou P,Jiao X F,Lv S X.Parallel remote state preparation of arbitrary single-qubit states via linear-optical elements by using hyperentangled Bell states as the quantum channel.Quantum Inf Process,2018,17:298
25 Huelga S F,Vaccaro J A,Chefles A,et al.Quantum remote control:Teleportation of unitary operations.Phys Rev A,2001,63:042303
26 He Y H,Lu Q C,Liao Y M,et al.Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states.Int J Theor Phys,2015,54:1726-1736
27 Fan Q B,Liu D D.Controlled remote implementation of partially unknown quantum operation.Sci China Ser G-Phys Mech Astron,2008,51:1661-1667
28 Lin J Y,He J G,Gao Y C,et al.Controlled remote implementation of an arbitrary single-qubit operation with partially entangled quantum channel.Int J Theor Phys,2017,56:1085-1095
29 Wang S,Liu Y,Chen J,et al.Deterministic single-qubit operation sharing with five-qubit cluster state.Quantum Inf Process,2013,12:2497-2507
30 Peng J.Tripartite operation sharing with five-qubit Brown state.Quantum Inf Process,2016,15:2465-2473
31 Tian D P,Tao Y J,Qin M.Teleportation of an arbitrary two-qudit state based on the non-maximally four-qudit cluster state.Sci China Ser G-Phys Mech Astron,2008,51:1523-1528
32 Lv S X,Zhao Z W,Zhou P.Joint remote control of an arbitrary single-qubit state by using a multiparticle entangled state as the quantum channel.Quantum Inf Process,2018,17:8
33 Barenco A,Bennett C H,Cleve R,et al.Elementary gates for quantum computation.Phys Rev A,1995,52:3457-3467
34 Ye M Y,Zhang Y S,Guo G C.Quantum entanglement and quantum operation(in Chinese).Sci Sin-Phys Mech Astron,2007,37:716-722[叶明勇,张永生,郭光灿.量子纠缠和量子操作.中国科学:物理学力学天文学,2007,37:716-722]
35 Chen L B,Lu H.Conclusive qudit states transformation implemented by remote parters(in Chinese).Sci Sin-Phys Mech Astron,2015,45:120301[陈立冰,路洪.远程协作实现高维量子态间的精确转换.中国科学:物理学力学天文学,2015,45:120301]
36 Chen L B,Lu H.Deterministic and controlled many-to-one and one-to-many remote quantum rotations via partially entangled quantum channels(in Chinese).Sci Sin-Phys Mech Astron,2014,44:1187-1195[陈立冰,路洪.利用部分纠缠的量子信道确定性地实现N→1和1→N的受控量子远程旋转.中国科学:物理学力学天文学,2014,44:1187-1195]
37 Xiang G Y,Li J,Guo G C.Teleporting a rotation on remote photons.Phys Rev A,2005,71:044304
38 Huang Y F,Ren X F,Zhang Y S,et al.Experimental teleportation of a quantum controlled-NOT gate.Phys Rev Lett,2004,93:240501
39 Eisert J,Jacobs K,Papadopoulos P,et al.Optimal local implementation of nonlocal quantum gates.Phys Rev A,2000,62:052317
40 Huelga S F,Plenio M B,Vaccaro J A.Remote control of restricted sets of operations:Teleportation of angles.Phys Rev A,2002,65:042316
41 Chen L B,Lu H.Nonlocal multi-target controlled-controlled gate using Greenberger-Horne-Zeilinger channel and qutrit catalysis.Chin Phys B,2015,24:070307
42 Chen L B,Lu H.Quantum networks for implementing locally and conclusively a nonlocal qudit Toffoli gate:Designing and optimizing(in Chinese).Sci Sin-Phys Mech Astron,2016,46:110301[陈立冰,路洪.确定性地实现非局域高维量子Toffoli门的网络设计与优化.中国科学:物理学力学天文学,2016,46:110301]
43 Chen L B,Lu H.Efficient nonlocal m-control and n-target controlled unitary gate using non-symmetric GHZ states.Int J Theor Phys,2018,57:706-714
44 Chou K S,Blumoff J Z,Wang C S,et al.Deterministic teleportation of a quantum gate between two logical qubits.Nature,2018,561:368-373
45 Bennett C H,Brassard G,Popescu S,et al.Purification of noisy entanglement and faithful teleportation via noisy channels.Phys Rev Lett,1996,76:722-725
46 Sheng Y B,Deng F G.Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement.Phys Rev A,2010,81:032307,arXiv:0912.0079
47 Sheng Y B,Deng F G.One-step deterministic polarization-entanglement purification using spatial entanglement.Phys Rev A,2010,82:044305,arXiv:1008.3509
48 Li X H,Deng F G,Zhou H Y.Faithful qubit transmission against collective noise without ancillary qubits.Appl Phys Lett,2007,91:144101,arXiv:0708.0068
49 Walton Z D,Abouraddy A F,Sergienko A V,et al.Decoherence-free subspaces in quantum key distribution.Phys Rev Lett,2003,91:087901
50 Deng F G,Li X H,Li T.Quantum error rejection and fault tolerant quantum communication(in Chinese).Acta Phys Sin,2018,67:130301[邓富国,李熙涵,李涛.基于光量子态避错及容错传输的量子通信.物理学报,2018,67:130301]
51 Yamamoto T,Shimamura J,?zdemir S K,et al.Faithful qubit distribution assisted by one additional qubit against collective noise.Phys Rev Lett,2005,95:040503
52 Li X H,Deng F G,Zhou H Y.Efficient quantum key distribution over a collective noise channel.Phys Rev A,2008,78:022321,arXiv:0808.0042
53 Dong L,Xiu X M,Gao Y J.Three-party controlled quantum teleportation with six-photon entangled states via collective noise channel.Acta Phys Pol B,2010,41:2377-2385
54 Gu B,Pei S X,Song B,et al.Secure quantum communication under joint noise(in Chinese).Sci Sin-Phys Mech Astron,2010,40:177-182[顾斌,裴世鑫,宋标,等.联合噪声下确定的安全量子通信.中国科学:物理学力学天文学,2010,40:177-182]
55 Li Z,Long L R,Zhou P,et al.Probabilistic multiparty-controlled teleportation of an arbitrary m-qubit state with a pure entangled quantum channel against collective noise.Sci China-Phys Mech Astron,2012,55:2445-2451
56 Zhou P,Li H W,Long L R.Probabilistic multiparty joint remote preparation of an arbitrary m-qubit state with a pure entangled channel against collective noise.Int J Theor Phys,2013,52:849-861
57 Takeuchi Y,Fujii K,Ikuta R,et al.Blind quantum computation over a collective-noise channel.Phys Rev A,2016,93:052307,arXiv:1505.04248
58 Sheng Y B,Zhou L.Blind quantum computation with a noise channel.Phys Rev A,2018,98:052343
59 Wang H F,Zhu A D,Zhang S,et al.Optically controlled phase gate and teleportation of a controlled-not gate for spin qubits in a quantum-dotmicrocavity coupled system.Phys Rev A,2013,87:062337,arXiv:1306.4737
60 Hu S,Cui W X,Wang D Y,et al.Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities.Sci Rep,2015,5:11321
61 Chen L B,Lu H.Implementing a nonlocal Toffoli gate using partially entangled qubit pairs.Int J Theor Phys,2011,50:3442-3450
62 Zhou P,Li X H,Deng F G,et al.Multiparty-controlled teleportation of an arbitrary m-qudit state with a pure entangled quantum channel.J Phys A-Math Theor,2007,40:13121-13130
63 Bourennane M,Eibl M,Gaertner S,et al.Decoherence-free quantum information processing with four-photon entangled states.Phys Rev Lett,2004,92:107901
64 Tsai C L,Hwang T.Semi-quantum key distribution robust against combined collective noise.Int J Theor Phys,2018,57:3410-3418