Research Article
BibTex RIS Cite

Year 2025, Volume: 67 Issue: 1, 74 - 83

Hasan Özgür Çıldıroğlu

https://doi.org/10.33769/aupse.1594115

Abstract

References

  • Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 47 (1935), 777, https://doi.org/10.1103/PhysRev.47.777.
  • Caspar, P., Verbanis, E., Oudot, E., Maring, N., Samara, F., Caloz, M., Perrenoud, M., Sekatski, P., Martin, A., et al., Heralded Distribution of Single-Photon Path Entanglement, Phys. Rev. Lett. 125, (2020), 110506, https://doi.org/10.1103/PhysRevLett.125.110506.
  • Matthews, J. C. F., Politi, A., Bonneau, D., O’Brien, J. L., Heralding two-photon and four-photon path entanglement on a chip, Phys. Rev. Lett., 107 (2011), 163602, https://doi.org/10.1103/PhysRevLett.107.163602.
  • Pant, M., Krovi, H., Towsley, D., Tassiulas, L., Jiang, L., Basu, P., Englund, D., Guha, S., Routing entanglement in the quantum internet, NPJ Quantum Inf., 5 (2019), Article no: 25, https://doi.org/10.1038/s41534-019-0139-x.
  • Jin, X. M., Peng, C. Z., Deng, Y., Sequential path entanglement for quantum metrology, Sci. Rep., 3 (2013), 1779, https://doi.org/10.1038/srep01779.
  • Shaik, A. B. Dajwi., Palla, P. Optical quantum technologies with hexagonal boron nitride single photon, Sci. Rep., 11 (2021), 12285, https://doi.org/10.1038/s41598-021-90804-4. Kim, H., Kwon, O., Moon, H. S., Experimental interference of uncorrelated photons, Sci. Rep., (2019), https://doi.org/10.1038/s41598-019-54504-4.
  • Krenn, M., Hochrainer, A., Lahiri, M., Zeilinger, A., Entanglement by path identity, Phys. Rev. Lett., 118 (2017), 080401, https://doi.org/10.1103/PhysRevLett.118.08040.
  • Guerreiro, T., Monteiro, F., Martin, A., Brask, J. B., Vertesi, T., Korzh, B., Caloz, M., Bussieres, F., Verma, V.B., Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection, Phys. Rev. Lett., 117 (2016), 070404, https://doi.org/10.1103/PhysRevLett.117.070404.
  • Lee, H., Kok, P., Cerf, N. J., Dowling, J. P., Linear optics and projective measurements alone suffice to create large-photon-number path entanglement, Phys. Rev. A, 65 (2002), 030101(R), https://doi.org/10.1103/PhysRevA.65.030101.
  • Wildfeuer, C. F., Lund, A. P., Dowling, J. P., Strong violations of BI for path-entangled number states, Phys. Rev. A, 76 (2007), 052101, https://doi.org/10.1103/PhysRevA.76.052101.
  • Cildiroglu, H. O. and Yilmazer, A. U., Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states, Phys. Lett. A 420 (2021): 127753, https://doi.org/10.1016/j.physleta.2021.127753.
  • Cildiroglu, H. O., Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases, Ann. Phys., 465 (2024), 169684, https://doi.org/10.1016/j.aop.2024.169684.
  • Cildiroglu, H. O., Concurrence-driven path entanglement in phase-modified interferometry, arXiv:2411.07131, (2024), https://doi.org/10.48550/arXiv.2411.07131.
  • Tunalioglu, M. E., Cildiroglu, H. O. and Yilmazer, A. U., On the geometric phases in entangled states, Commun.Fac.Sci.Univ.Ank.Series A2-A3, 65 (2) (2023), 142-151, https://doi.org/10.33769/aupse.1286632.
  • Boto, A. N., Kok, P., Abrams, D. S., Braunstein, S. L., Williams, C. P. and Dowling, J. P., Quantum interferometric optical lithography, Phys. Rev. Lett., 85 (2000), 2733, https://doi.org/10.1103/PhysRevLett.85.2733.
  • Kok, P., Boto, A. N., Abrams, D. S., Braunstein, S. L., Williams, C. P. and Dowling, J. P., Quantum-interferometric optical lithography, Phys. Rev. A, 63 (2001), 063407, https://doi.org/10.1103/PhysRevA.63.063407.
  • Kysela, J., Erhard, M., Hochrainer, A., Krenn, M., Zeilinger, A., Path identity as a source of high dimensional entanglement, PNAS, 117 (42) (2020), 26118-26122, https://doi.org/10.1073/pnas.2011405117.
  • Solntsev, A. S., Sukhorukov, A. A., Path-entangled photon sources on nonlinear chips, Rev. Phys., (2016), https://doi.org/10.1016/j.revip.2016.11.003.
  • Menzel, E. P., Di Candia, R., Deppe, F., Eder, P., Zhong, L., Ihmig, M., Haeberlein, M., Baust, A., Hoffmann, E., Path entanglement of continuous-variable quantum MW, Phys. Rev. Lett., 109 (2012), 250502, https://doi.org/10.1103/PhysRevLett.109.250502.
  • Dowling, J. P., Correlated input-port, matter-wave interferometer, Phys. Rev. A, 57 (1998), 4736, https://doi.org/10.1103/PhysRevA.57.4736.
  • Eisenberg, H. S., Hodelin, J. F., Khoury, G., Bouwmeester, D., Multiphoton path entanglement by nonlocal bunching, Phys. Rev. Lett., 94 (2005), 090502, https://doi.org/10.1103/PhysRevLett.94.090502.
  • Cable, H., Dowling, J. P., Efficient generation of large number-path entanglement, Phys. Rev. Lett., 99 (2007), 163604, https://doi.org/10.1103/PhysRevLett.99.163604.
  • Jozsa, R., Fidelity for mixed quantum states, J. Mod. Opt., 41 (12) (1994), 2315-2323, https://doi.org/10.1080/09500349414552171.
  • Schumacher, B., Sending quantum entanglement through noisy channels, Phys. Rev. A, 54 (1996), 2614, https://doi.org/10.48550/arXiv.quant-ph/9604023.
  • Wootters, W., Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80 (1998), 2245, https://doi.org/10.1103/PhysRevLett.80.2245.
  • Vedral, V., Plenio, M., Rippin, M., Quantifying entanglement, Phys. Rev. Lett., 78 (1997), 2275, https://doi.org/10.1103/PhysRevLett.78.2275.
  • Vidal, G., Werner, R., Computable measure of entanglement, Phys. Rev. A, 65 (2002), 032314, https://doi.org/10.1103/PhysRevA.65.032314.
  • Plenio, M. B. and Virmani, S., An introduction to entanglement measures, Quantum Information & Comp., 7 (1) (2007), 1-51, https://doi.org/10.1007/978-3-319-04063-9_8.
  • Uhlmann, A., Fidelity and concurrence of conjugated states, Phys. Rev. A, 62 (2000), 032307, https://doi.org/10.1103/PhysRevA.62.032307.
  • Rungta, P., Buzek, V., Caves, C. M., Hillery, M., Milburn, G. J., Universal state inversion and concurrence in arbitrary dimensions, Phys. Rev. A, 64 (2001), 042315, https://doi.org/10.1103/PhysRevA.64.042315.
  • Horodecki, R., Horodecki, P., Horodecki, M., Quantum entanglement, Rev. Mod. Phys., 81 (2009), 865-942, https://doi.org/10.1103/RevModPhys.81.865.
  • Preskill, J., Quantum computing in the NISQ era and beyond, Quantum, 2 (2018), 79, https://doi.org/10.22331/q-2018-08-06-79.
  • Salhov, A., Cao, Q., Cai, J., Retzker, A., Jelezko, F. and Genov, G., Phys. Rev. Lett., 132 (22) (2024), 223601, https://doi.org/10.1103/PhysRevLett.132.223601.
  • Xu, Q., Bonilla Ataides, J. P., Pattison, C. A., Constant-overhead fault-tolerant comp., Nat. Phys., 20 (2024), 1084-1090, https://doi.org/10.1038/s41567-024-02479-z.
  • Scarani, V., Iblisdir, S., Gisin, N. and Acin, A., Quantum cloning, Rev. Mod. Phys., 77 (2005), 1225-1256, https://doi.org/10.1103/RevModPhys.77.1225.

Fidelity analysis of path entangled two-quanton systems

Year 2025, Volume: 67 Issue: 1, 74 - 83

Hasan Özgür Çıldıroğlu

https://doi.org/10.33769/aupse.1594115

Abstract

Path (momentum) entanglement, arising from the spatial correlations of quantons, constitutes a cornerstone of quantum communication, metrology, and advanced interferometry. Despite its profound importance, the quantitative evaluation of path entanglement remains an intricate task, particularly under transformations imposed by interferometric setups. This study explores the fidelity of path entanglement in two interferometric configurations, P-BS and BS-P-BS, for spatially correlated two-quanton systems. Fidelity, which measures the preservation of quantum correlations, is analyzed alongside concurrence to capture the dynamics of entanglement under phase retarder manipulations. Our findings reveal contrasting behaviors between the two setups: while the P-BS configuration shows a decrease in fidelity with increasing concurrence, the BS-P-BS setup achieves maximum fidelity for maximally entangled states with carefully tuned retarder phases. These findings underscore the robustness of the BS-P-BS architecture in maintaining quantum correlations, rendering it a compelling candidate for quantum teleportation and high-fidelity quantum channel implementations. Furthermore, the interplay between retarder phases, concurrence, and fidelity offers novel insights for optimizing interferometric designs in advanced quantum information processing applications.

Keywords

Path-Entanglement momentum correlation fidelity

References

  • Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 47 (1935), 777, https://doi.org/10.1103/PhysRev.47.777.
  • Caspar, P., Verbanis, E., Oudot, E., Maring, N., Samara, F., Caloz, M., Perrenoud, M., Sekatski, P., Martin, A., et al., Heralded Distribution of Single-Photon Path Entanglement, Phys. Rev. Lett. 125, (2020), 110506, https://doi.org/10.1103/PhysRevLett.125.110506.
  • Matthews, J. C. F., Politi, A., Bonneau, D., O’Brien, J. L., Heralding two-photon and four-photon path entanglement on a chip, Phys. Rev. Lett., 107 (2011), 163602, https://doi.org/10.1103/PhysRevLett.107.163602.
  • Pant, M., Krovi, H., Towsley, D., Tassiulas, L., Jiang, L., Basu, P., Englund, D., Guha, S., Routing entanglement in the quantum internet, NPJ Quantum Inf., 5 (2019), Article no: 25, https://doi.org/10.1038/s41534-019-0139-x.
  • Jin, X. M., Peng, C. Z., Deng, Y., Sequential path entanglement for quantum metrology, Sci. Rep., 3 (2013), 1779, https://doi.org/10.1038/srep01779.
  • Shaik, A. B. Dajwi., Palla, P. Optical quantum technologies with hexagonal boron nitride single photon, Sci. Rep., 11 (2021), 12285, https://doi.org/10.1038/s41598-021-90804-4. Kim, H., Kwon, O., Moon, H. S., Experimental interference of uncorrelated photons, Sci. Rep., (2019), https://doi.org/10.1038/s41598-019-54504-4.
  • Krenn, M., Hochrainer, A., Lahiri, M., Zeilinger, A., Entanglement by path identity, Phys. Rev. Lett., 118 (2017), 080401, https://doi.org/10.1103/PhysRevLett.118.08040.
  • Guerreiro, T., Monteiro, F., Martin, A., Brask, J. B., Vertesi, T., Korzh, B., Caloz, M., Bussieres, F., Verma, V.B., Demonstration of Einstein-Podolsky-Rosen steering using single-photon path entanglement and displacement-based detection, Phys. Rev. Lett., 117 (2016), 070404, https://doi.org/10.1103/PhysRevLett.117.070404.
  • Lee, H., Kok, P., Cerf, N. J., Dowling, J. P., Linear optics and projective measurements alone suffice to create large-photon-number path entanglement, Phys. Rev. A, 65 (2002), 030101(R), https://doi.org/10.1103/PhysRevA.65.030101.
  • Wildfeuer, C. F., Lund, A. P., Dowling, J. P., Strong violations of BI for path-entangled number states, Phys. Rev. A, 76 (2007), 052101, https://doi.org/10.1103/PhysRevA.76.052101.
  • Cildiroglu, H. O. and Yilmazer, A. U., Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states, Phys. Lett. A 420 (2021): 127753, https://doi.org/10.1016/j.physleta.2021.127753.
  • Cildiroglu, H. O., Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases, Ann. Phys., 465 (2024), 169684, https://doi.org/10.1016/j.aop.2024.169684.
  • Cildiroglu, H. O., Concurrence-driven path entanglement in phase-modified interferometry, arXiv:2411.07131, (2024), https://doi.org/10.48550/arXiv.2411.07131.
  • Tunalioglu, M. E., Cildiroglu, H. O. and Yilmazer, A. U., On the geometric phases in entangled states, Commun.Fac.Sci.Univ.Ank.Series A2-A3, 65 (2) (2023), 142-151, https://doi.org/10.33769/aupse.1286632.
  • Boto, A. N., Kok, P., Abrams, D. S., Braunstein, S. L., Williams, C. P. and Dowling, J. P., Quantum interferometric optical lithography, Phys. Rev. Lett., 85 (2000), 2733, https://doi.org/10.1103/PhysRevLett.85.2733.
  • Kok, P., Boto, A. N., Abrams, D. S., Braunstein, S. L., Williams, C. P. and Dowling, J. P., Quantum-interferometric optical lithography, Phys. Rev. A, 63 (2001), 063407, https://doi.org/10.1103/PhysRevA.63.063407.
  • Kysela, J., Erhard, M., Hochrainer, A., Krenn, M., Zeilinger, A., Path identity as a source of high dimensional entanglement, PNAS, 117 (42) (2020), 26118-26122, https://doi.org/10.1073/pnas.2011405117.
  • Solntsev, A. S., Sukhorukov, A. A., Path-entangled photon sources on nonlinear chips, Rev. Phys., (2016), https://doi.org/10.1016/j.revip.2016.11.003.
  • Menzel, E. P., Di Candia, R., Deppe, F., Eder, P., Zhong, L., Ihmig, M., Haeberlein, M., Baust, A., Hoffmann, E., Path entanglement of continuous-variable quantum MW, Phys. Rev. Lett., 109 (2012), 250502, https://doi.org/10.1103/PhysRevLett.109.250502.
  • Dowling, J. P., Correlated input-port, matter-wave interferometer, Phys. Rev. A, 57 (1998), 4736, https://doi.org/10.1103/PhysRevA.57.4736.
  • Eisenberg, H. S., Hodelin, J. F., Khoury, G., Bouwmeester, D., Multiphoton path entanglement by nonlocal bunching, Phys. Rev. Lett., 94 (2005), 090502, https://doi.org/10.1103/PhysRevLett.94.090502.
  • Cable, H., Dowling, J. P., Efficient generation of large number-path entanglement, Phys. Rev. Lett., 99 (2007), 163604, https://doi.org/10.1103/PhysRevLett.99.163604.
  • Jozsa, R., Fidelity for mixed quantum states, J. Mod. Opt., 41 (12) (1994), 2315-2323, https://doi.org/10.1080/09500349414552171.
  • Schumacher, B., Sending quantum entanglement through noisy channels, Phys. Rev. A, 54 (1996), 2614, https://doi.org/10.48550/arXiv.quant-ph/9604023.
  • Wootters, W., Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80 (1998), 2245, https://doi.org/10.1103/PhysRevLett.80.2245.
  • Vedral, V., Plenio, M., Rippin, M., Quantifying entanglement, Phys. Rev. Lett., 78 (1997), 2275, https://doi.org/10.1103/PhysRevLett.78.2275.
  • Vidal, G., Werner, R., Computable measure of entanglement, Phys. Rev. A, 65 (2002), 032314, https://doi.org/10.1103/PhysRevA.65.032314.
  • Plenio, M. B. and Virmani, S., An introduction to entanglement measures, Quantum Information & Comp., 7 (1) (2007), 1-51, https://doi.org/10.1007/978-3-319-04063-9_8.
  • Uhlmann, A., Fidelity and concurrence of conjugated states, Phys. Rev. A, 62 (2000), 032307, https://doi.org/10.1103/PhysRevA.62.032307.
  • Rungta, P., Buzek, V., Caves, C. M., Hillery, M., Milburn, G. J., Universal state inversion and concurrence in arbitrary dimensions, Phys. Rev. A, 64 (2001), 042315, https://doi.org/10.1103/PhysRevA.64.042315.
  • Horodecki, R., Horodecki, P., Horodecki, M., Quantum entanglement, Rev. Mod. Phys., 81 (2009), 865-942, https://doi.org/10.1103/RevModPhys.81.865.
  • Preskill, J., Quantum computing in the NISQ era and beyond, Quantum, 2 (2018), 79, https://doi.org/10.22331/q-2018-08-06-79.
  • Salhov, A., Cao, Q., Cai, J., Retzker, A., Jelezko, F. and Genov, G., Phys. Rev. Lett., 132 (22) (2024), 223601, https://doi.org/10.1103/PhysRevLett.132.223601.
  • Xu, Q., Bonilla Ataides, J. P., Pattison, C. A., Constant-overhead fault-tolerant comp., Nat. Phys., 20 (2024), 1084-1090, https://doi.org/10.1038/s41567-024-02479-z.
  • Scarani, V., Iblisdir, S., Gisin, N. and Acin, A., Quantum cloning, Rev. Mod. Phys., 77 (2005), 1225-1256, https://doi.org/10.1103/RevModPhys.77.1225.
There are 35 citations in total.

Details

Primary Language English
Subjects Quantum Information, Computation and Communication, Foundations of Quantum Mechanics, Quantum Optics and Quantum Optomechanics
Journal Section Research Articles
Authors

Hasan Özgür Çıldıroğlu 0000-0003-0246-1102

Publication Date
Submission Date November 30, 2024
Acceptance Date February 24, 2025
Published in Issue Year 2025 Volume: 67 Issue: 1

Cite

APA Çıldıroğlu, H. Ö. (n.d.). Fidelity analysis of path entangled two-quanton systems. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, 67(1), 74-83. https://doi.org/10.33769/aupse.1594115
AMA Çıldıroğlu HÖ. Fidelity analysis of path entangled two-quanton systems. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 67(1):74-83. doi:10.33769/aupse.1594115
Chicago Çıldıroğlu, Hasan Özgür. “Fidelity Analysis of Path Entangled Two-Quanton Systems”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 67, no. 1 n.d.: 74-83. https://doi.org/10.33769/aupse.1594115.
EndNote Çıldıroğlu HÖ Fidelity analysis of path entangled two-quanton systems. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 67 1 74–83.
IEEE H. Ö. Çıldıroğlu, “Fidelity analysis of path entangled two-quanton systems”, Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng., vol. 67, no. 1, pp. 74–83, doi: 10.33769/aupse.1594115.
ISNAD Çıldıroğlu, Hasan Özgür. “Fidelity Analysis of Path Entangled Two-Quanton Systems”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 67/1 (n.d.), 74-83. https://doi.org/10.33769/aupse.1594115.
JAMA Çıldıroğlu HÖ. Fidelity analysis of path entangled two-quanton systems. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng.;67:74–83.
MLA Çıldıroğlu, Hasan Özgür. “Fidelity Analysis of Path Entangled Two-Quanton Systems”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, vol. 67, no. 1, pp. 74-83, doi:10.33769/aupse.1594115.
Vancouver Çıldıroğlu HÖ. Fidelity analysis of path entangled two-quanton systems. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 67(1):74-83.

Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.