Genelleştirilmiş Kuantum Işınlama Protokolü

Emir Oğuz Kaya

doi:10.21205/deufmd.2023257306

Research Article

Generalized Quantum Teleportation Protocol

Year 2023, Volume: 25 Issue: 73, 69 - 80, 26.01.2023

Emir Oğuz Kaya

https://doi.org/10.21205/deufmd.2023257306

Abstract

Within the scope of this study, generalization of the single qubit (quantum bit) teleportation protocol to multi-qubit systems has been examined. Then, the possibilities of teleporting to more than one target were discussed and a protocol for this was proposed. Within the scope of the developed theoretical framework, the generalization of quantum logic gates that modify qubits is also discussed. General versions of these quantum logic gates have been created and they have been shown to work for special cases in the literature. It has been determined that the equations formed in the theoretical framework established as a result of the generalization of the teleportation to many qubits and many targets, contain a pattern, and a way to carry out the protocol without dealing with complex tensor products one by one is proposed through this pattern.
Within the scope of the study, Python computer programs were created for multi-qubit - single target, multi-qubit - multi-target protocols. It has been observed that the created programs successfully produce the results predicted by the theoretical framework presented. Through these programs, it is possible to perform long and error-free mathematical operations in a short time. The generated program results also prove the existence of the above-mentioned pattern.

Keywords

Quantum Teleportation, Qubit, Quantum Logic Gate

References

1. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.,1993,"Teleporting an unknown quantum state via dual classic and Einstein–Podolsky–Rosen channels", Phys. Rev. Lett. 70, 1895–1899
2. Ikram, M., Zhu, S.Y., Zubairy, M.S.,2000, "Quantum teleportation of an entangled state" Phys. Rev. A. 62, 022307
3. Rigolin, G. ,2005, "Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement", Phys. Rev. A. 71, 032303
4. Yang, C.P., Guo, G.C. ,2000, " Multiparticle generalization of teleportation" Chin. Phys. Lett. 17, 162–164
5. Lee, J., Min, H., Oh, S.D. ,2002, " Multipartite entanglement for entanglement teleportation", Phys. Rev. A. 66,052318
6. Cheung, C.Y., Zhang, Z.J. ,2009, " Criterion for faithful teleportation with an arbitrary multiparticle channel", Phys.Rev. A. 80, 022327
7. Zhao,M.J., 2011," Faithful teleportation with arbitrary pure or mixed resource states" J. Phys. AMath. Theor.44, 215302
8. Praksh, H., Verma, V.,2012,"Minimum assured fidelity and minimum average fidelity in quantum teleportation ofsingle qubit using non-maximally entangled states", Quantum Inf. Process. 11, 1951–1959
9. Meng, Q., Long, X.S., Yue, Z.X.,2012," Standard teleportation of one-qubit state and partial teleportation of twoqubitstate via X-state" Commun. Theor. Phys. 57, 201–204
10. Verma, V., Prakash, H. ,2016," Standard quantum teleportation and controlled quantum teleportation of arbitrary N-qubit information state" Int. J. Theo. Phy. 55, 2061–2070
11. Cai, T., Jiang, M.,2018," Improving the teleportation scheme of three-qubit state with a four-qubit Quantum Channe", Int. J. Theor. Phys. 57, 131–137
12. Karlson, A., Bourennane, M.,1998," Quantum teleportation using three-particle entanglement" Phys. Rev. A. 58, 4394–4400
13. Yang, C.P., Chu, S.I., Han, S. ,2007," Efficient many-party controlled teleportation of multiqubit quantum information via entanglement" Phys. Rev. A. 70, 022329
14. Man, Z.X., Xia, Y.J., An, N.B. ,2007," Genuine multiqubit entanglement and controlled teleportation" Phys. Rev. A. 75, 052306
15. Yan, F., Wang, D.,2003," Probabilistic and controlled teleportation of unknown quantum states", Phys. Lett. A. 316, 297–303
16. Dong, J., Teng, J.F. ,2008," Controlled teleportation of an arbitrary n-qudit state using non-maximally entangled GHZ states", Eur. Phys. J. D. 49, 129–134
17. Nie, Y.Y., Hong, Z.H., Huang, Y.B., Yi, X.J., Li, S.S.,2009," Non-maximally entangled controlled teleportation usingfourparticleskümestates", Int. J. Theor. Phys. 48, 1485–1490
18. Shi, R.H., Huang, L.S., Yang, W., Zhong, H.,2011," Controlled quantum perfect teleportation of multiple arbitrary multi-qubit states", Sci. China. 54, 2208–2216
19. Li, Y.H., Li, X.L., Nie, L.P., Sang, M.H.,2016," Quantum teleportation of three and four-qubit stateusingmultiqubitkümestates", Int. J. Theor. Phys. 55, 1820–1823
20. Li, Y.H., Sang, M.H., Wang, X.P., Nie, Y.Y.,2016," Quantum teleportation of a four-qubit state byusingsix-qubitkümestate", Int. J. Theor. Phys. 55, 3547–3550
21. Cao, L., Xue, S., Jiang,M.,2020," Teleportation of an unknownfour-qubitkümestatebased on kümestateswith minimum resource", IEEE Access. 8, 81447–81457
22. Li, M., Zhao, N., Chen, N., Zhu, C.H., Pei, C.X. ,2017," Quantum teleportation of five-qubit state", Int. J. Theor. Phys. 56, 2710–2715
23. Yang, Y., Jiang, M., Zhou, L.L. ,2018," Improving the teleportation scheme of five-qubit state with a seven-qubit Quantum Channel", Int. J. Theor. Phys. 57, 3485–3491
24. Choudhury, B.S., Dhara, A., Samanta, S. ,2017," Teleportation of five-qubit state using six-qubit state", Phys. Part. Nucl. Lett. 14, 644–646
25. Bouwmeester, D., Pan, J.W., Mattle, K., Ebil, M., Weinfurter, H., Zeilinger, A., 1997," Experimental quantum teleportation", Nature (London). 390, 575–579
26. Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S. ,1998," Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels", Phys. Rev. Lett. 80, 1121–1125
27. Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S. ,1998," Unconditional quantum teleportation", Science. 282, 706–709
28. Lee, H.W. ,2001," Total teleportation of an entangled state", Phys. Rev. A. 64, 014302
29. Verma, V., Singh, N., Singh, R.S., 2021, "Improvement on Quantum Teleportation of Three and Four Qubit States Using Multi-QubitKümeStates", Int. J. Theor. Phys. 60, 3973-3981
30. Li, M., Zhao, N., Chen, N., Zhu, C.H., Pei, C.X. ,2018," Quantum teleportation of eight-qubit stateviasix-qubitkümestate", Int. J. Theor. Phys. 57, 516-522
31. Sang, M.H.,2016," Bidirectional quantum teleportation byusingfive-qubitkümestate", Int. J. Theor. Phys. 55(3), 1333–1335
32. Li, Y.H., Jin, X.M.,2016," Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments", Quantum. Inf. Process. 15(2), 929–945
33. Fatahi, N., Naseri, M., 2021, "Quantum teleportation of a N-qubit entangled state by using a (N+1)-qubitkümestate", Quantum. Inf. Process. 20, 367
34. Jin, X.M., Ren, J.G., Yang, B., Yi, Z.H., Zhou, F., Xu, X.F., Wang, S.K., Yang, D., Hu, Y.F., Jiang, S.,Yang, T., Yin, H., Chen, K., Peng, C.Z., Pan, J.W. ,2010, "Experimental free-space quantum teleportation", Nat. Photonics 4, 376–381
35. Metcalf, B.J., Spring, J.B., Humphreys, P.C., Thomas-Peter, N., Barbieri, M., Kolthammer, W.S., Jin,X.M., Langford, N.K., Kundys, D., Gates, J.C., Smith, B.J., Smith, P.G.R., Walmsley, I.A.,2014,"Quantum teleportation on a photonic chip", Nat. Photonics 8, 770–774
36. Duan, Y., Zha, X., Sun, X., Xia, J., 2014, "Bidirectional quantum controlled teleportation via a maximally seven-qubit entangled state", Int. J. Theor. Phys. 53, 2697-2707
37. Cohn ,J.H.E., 1965,"Hadamard matrices and some generalisations", Amer. Math. Monthly, 72:515–518
38. Hedayat, A., Wallis, W.D.,1978, "Hadamard matrices and their applicalions", The. Annals. of. Statistics. 6, 1184-1238
39. Rakotonirina, C., Rasamizafy, S., 2016, "3x3 Kronecker pauli matrices", A Peer Reviewed International Research Journal. 6, 127-134
40. Rakotonirina, C., 2018,"Rectangle gell-mann matrices ", Institut Sup´erieur de Technologie d’AntananarivoIST-T, BP 8122
41. Yang, C. P., Chu, S. I., Han, S., 2005, "Efficient many-party controlled teleportation of multi-qubit quantum informationviaentanglement", arXiv:quant-ph/0402138v2
42. Bolokian, M.,Housmand, M., Sadeghizadeh, M. S., Parvaneh, M., 2020, "Multi-Party Quantum TeleportationwithSelectiveReceiver", Int. J. Theor. Phys. 60, 828-837

Genelleştirilmiş Kuantum Işınlama Protokolü

Year 2023, Volume: 25 Issue: 73, 69 - 80, 26.01.2023

Emir Oğuz Kaya

https://doi.org/10.21205/deufmd.2023257306

Abstract

Bu çalışma kapsamında literatürde var olan tek kubit(kuantum bit) ışınlanma/telenakil (quantum teleportation) protokolünün çok kubit sistemlere genellenmesi incelenmiştir. Ardından, birden fazla hedefe telenakil olanakları tartışılarak, buna dair bir protokol önerilmiştir. Geliştirilen teorik çerçeve kapsamında, kubitler üzerinde değişiklik yapan kuantum mantık kapılarının da genellenmesi tartışılmıştır. Söz konusu kuantum mantık kapılarının genel versiyonları oluşturulmuş olup, literatürdeki özel durumlar için çalıştıkları gösterilmiştir. Işınlanmanın çok kubit-çok hedefe genellenmesi sonucu kurulan teorik çerçevede oluşan denklemlerin bir örüntü içerdiği belirlenmiş olup, bu örüntü aracılığı ile karmaşık tensör çarpımları ile tek tek uğraşmaksızın da protokolün gerçekleştirilebileceği bir yol önerilmiştir.
Çalışma kapsamında çok kubit - tek hedef, çok kubit – çok hedef protokollerine yönelik Python bilgisayar programları oluşturulmuştur. Oluşturulan programların, sunulan teorik çerçevenin ön gördüğü sonuçları başarılı bir şekilde ürettiği gözlenmiştir. Bu programlar aracılığı ile, uzun ve hata yapma olasılığı yüksek matematiksel işlemlerin kısa sürede ve hatasız yapılabilmesinin olanağı yaratılmıştır. Oluşturulan program sonuçları aynı zamanda, yukarıda bahsedilen örüntünün varlığını kanıtlamaktadır.

Keywords

Kuantum Işınlaması, Kuantum Bit, Kuantum Mantık Kapısı, Quantum Teleportation, Qubit, Quantum Logic Gate

References

1. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.,1993,"Teleporting an unknown quantum state via dual classic and Einstein–Podolsky–Rosen channels", Phys. Rev. Lett. 70, 1895–1899
2. Ikram, M., Zhu, S.Y., Zubairy, M.S.,2000, "Quantum teleportation of an entangled state" Phys. Rev. A. 62, 022307
3. Rigolin, G. ,2005, "Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement", Phys. Rev. A. 71, 032303
4. Yang, C.P., Guo, G.C. ,2000, " Multiparticle generalization of teleportation" Chin. Phys. Lett. 17, 162–164
5. Lee, J., Min, H., Oh, S.D. ,2002, " Multipartite entanglement for entanglement teleportation", Phys. Rev. A. 66,052318
6. Cheung, C.Y., Zhang, Z.J. ,2009, " Criterion for faithful teleportation with an arbitrary multiparticle channel", Phys.Rev. A. 80, 022327
7. Zhao,M.J., 2011," Faithful teleportation with arbitrary pure or mixed resource states" J. Phys. AMath. Theor.44, 215302
8. Praksh, H., Verma, V.,2012,"Minimum assured fidelity and minimum average fidelity in quantum teleportation ofsingle qubit using non-maximally entangled states", Quantum Inf. Process. 11, 1951–1959
9. Meng, Q., Long, X.S., Yue, Z.X.,2012," Standard teleportation of one-qubit state and partial teleportation of twoqubitstate via X-state" Commun. Theor. Phys. 57, 201–204
10. Verma, V., Prakash, H. ,2016," Standard quantum teleportation and controlled quantum teleportation of arbitrary N-qubit information state" Int. J. Theo. Phy. 55, 2061–2070
11. Cai, T., Jiang, M.,2018," Improving the teleportation scheme of three-qubit state with a four-qubit Quantum Channe", Int. J. Theor. Phys. 57, 131–137
12. Karlson, A., Bourennane, M.,1998," Quantum teleportation using three-particle entanglement" Phys. Rev. A. 58, 4394–4400
13. Yang, C.P., Chu, S.I., Han, S. ,2007," Efficient many-party controlled teleportation of multiqubit quantum information via entanglement" Phys. Rev. A. 70, 022329
14. Man, Z.X., Xia, Y.J., An, N.B. ,2007," Genuine multiqubit entanglement and controlled teleportation" Phys. Rev. A. 75, 052306
15. Yan, F., Wang, D.,2003," Probabilistic and controlled teleportation of unknown quantum states", Phys. Lett. A. 316, 297–303
16. Dong, J., Teng, J.F. ,2008," Controlled teleportation of an arbitrary n-qudit state using non-maximally entangled GHZ states", Eur. Phys. J. D. 49, 129–134
17. Nie, Y.Y., Hong, Z.H., Huang, Y.B., Yi, X.J., Li, S.S.,2009," Non-maximally entangled controlled teleportation usingfourparticleskümestates", Int. J. Theor. Phys. 48, 1485–1490
18. Shi, R.H., Huang, L.S., Yang, W., Zhong, H.,2011," Controlled quantum perfect teleportation of multiple arbitrary multi-qubit states", Sci. China. 54, 2208–2216
19. Li, Y.H., Li, X.L., Nie, L.P., Sang, M.H.,2016," Quantum teleportation of three and four-qubit stateusingmultiqubitkümestates", Int. J. Theor. Phys. 55, 1820–1823
20. Li, Y.H., Sang, M.H., Wang, X.P., Nie, Y.Y.,2016," Quantum teleportation of a four-qubit state byusingsix-qubitkümestate", Int. J. Theor. Phys. 55, 3547–3550
21. Cao, L., Xue, S., Jiang,M.,2020," Teleportation of an unknownfour-qubitkümestatebased on kümestateswith minimum resource", IEEE Access. 8, 81447–81457
22. Li, M., Zhao, N., Chen, N., Zhu, C.H., Pei, C.X. ,2017," Quantum teleportation of five-qubit state", Int. J. Theor. Phys. 56, 2710–2715
23. Yang, Y., Jiang, M., Zhou, L.L. ,2018," Improving the teleportation scheme of five-qubit state with a seven-qubit Quantum Channel", Int. J. Theor. Phys. 57, 3485–3491
24. Choudhury, B.S., Dhara, A., Samanta, S. ,2017," Teleportation of five-qubit state using six-qubit state", Phys. Part. Nucl. Lett. 14, 644–646
25. Bouwmeester, D., Pan, J.W., Mattle, K., Ebil, M., Weinfurter, H., Zeilinger, A., 1997," Experimental quantum teleportation", Nature (London). 390, 575–579
26. Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S. ,1998," Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels", Phys. Rev. Lett. 80, 1121–1125
27. Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S. ,1998," Unconditional quantum teleportation", Science. 282, 706–709
28. Lee, H.W. ,2001," Total teleportation of an entangled state", Phys. Rev. A. 64, 014302
29. Verma, V., Singh, N., Singh, R.S., 2021, "Improvement on Quantum Teleportation of Three and Four Qubit States Using Multi-QubitKümeStates", Int. J. Theor. Phys. 60, 3973-3981
30. Li, M., Zhao, N., Chen, N., Zhu, C.H., Pei, C.X. ,2018," Quantum teleportation of eight-qubit stateviasix-qubitkümestate", Int. J. Theor. Phys. 57, 516-522
31. Sang, M.H.,2016," Bidirectional quantum teleportation byusingfive-qubitkümestate", Int. J. Theor. Phys. 55(3), 1333–1335
32. Li, Y.H., Jin, X.M.,2016," Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments", Quantum. Inf. Process. 15(2), 929–945
33. Fatahi, N., Naseri, M., 2021, "Quantum teleportation of a N-qubit entangled state by using a (N+1)-qubitkümestate", Quantum. Inf. Process. 20, 367
34. Jin, X.M., Ren, J.G., Yang, B., Yi, Z.H., Zhou, F., Xu, X.F., Wang, S.K., Yang, D., Hu, Y.F., Jiang, S.,Yang, T., Yin, H., Chen, K., Peng, C.Z., Pan, J.W. ,2010, "Experimental free-space quantum teleportation", Nat. Photonics 4, 376–381
35. Metcalf, B.J., Spring, J.B., Humphreys, P.C., Thomas-Peter, N., Barbieri, M., Kolthammer, W.S., Jin,X.M., Langford, N.K., Kundys, D., Gates, J.C., Smith, B.J., Smith, P.G.R., Walmsley, I.A.,2014,"Quantum teleportation on a photonic chip", Nat. Photonics 8, 770–774
36. Duan, Y., Zha, X., Sun, X., Xia, J., 2014, "Bidirectional quantum controlled teleportation via a maximally seven-qubit entangled state", Int. J. Theor. Phys. 53, 2697-2707
37. Cohn ,J.H.E., 1965,"Hadamard matrices and some generalisations", Amer. Math. Monthly, 72:515–518
38. Hedayat, A., Wallis, W.D.,1978, "Hadamard matrices and their applicalions", The. Annals. of. Statistics. 6, 1184-1238
39. Rakotonirina, C., Rasamizafy, S., 2016, "3x3 Kronecker pauli matrices", A Peer Reviewed International Research Journal. 6, 127-134
40. Rakotonirina, C., 2018,"Rectangle gell-mann matrices ", Institut Sup´erieur de Technologie d’AntananarivoIST-T, BP 8122
41. Yang, C. P., Chu, S. I., Han, S., 2005, "Efficient many-party controlled teleportation of multi-qubit quantum informationviaentanglement", arXiv:quant-ph/0402138v2
42. Bolokian, M.,Housmand, M., Sadeghizadeh, M. S., Parvaneh, M., 2020, "Multi-Party Quantum TeleportationwithSelectiveReceiver", Int. J. Theor. Phys. 60, 828-837

There are 42 citations in total.

Details

Primary Language	Turkish
Journal Section	Research Article
Authors	Emir Oğuz Kaya 0000-0002-3321-3534
Publication Date	January 26, 2023
Published in Issue	Year 2023 Volume: 25 Issue: 73

Cite

APA	Kaya, E. O. (2023). Genelleştirilmiş Kuantum Işınlama Protokolü. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 25(73), 69-80. https://doi.org/10.21205/deufmd.2023257306
AMA	Kaya EO. Genelleştirilmiş Kuantum Işınlama Protokolü. DEUFMD. January 2023;25(73):69-80. doi:10.21205/deufmd.2023257306
Chicago	Kaya, Emir Oğuz. “Genelleştirilmiş Kuantum Işınlama Protokolü”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 25, no. 73 (January 2023): 69-80. https://doi.org/10.21205/deufmd.2023257306.
EndNote	Kaya EO (January 1, 2023) Genelleştirilmiş Kuantum Işınlama Protokolü. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 25 73 69–80.
IEEE	E. O. Kaya, “Genelleştirilmiş Kuantum Işınlama Protokolü”, DEUFMD, vol. 25, no. 73, pp. 69–80, 2023, doi: 10.21205/deufmd.2023257306.
ISNAD	Kaya, Emir Oğuz. “Genelleştirilmiş Kuantum Işınlama Protokolü”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 25/73 (January 2023), 69-80. https://doi.org/10.21205/deufmd.2023257306.
JAMA	Kaya EO. Genelleştirilmiş Kuantum Işınlama Protokolü. DEUFMD. 2023;25:69–80.
MLA	Kaya, Emir Oğuz. “Genelleştirilmiş Kuantum Işınlama Protokolü”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, vol. 25, no. 73, 2023, pp. 69-80, doi:10.21205/deufmd.2023257306.
Vancouver	Kaya EO. Genelleştirilmiş Kuantum Işınlama Protokolü. DEUFMD. 2023;25(73):69-80.

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Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.