Research Article
BibTex RIS Cite

Year 2023, Volume: 65 Issue: 2, 142 - 151, 29.12.2023

Melik Emirhan Tunalıoğlu , Hasan Özgür Çıldıroğlu , Ali Ulvi Yılmazer

https://doi.org/10.33769/aupse.1286632

Abstract

References

  • Ehrenberg, W., Siday, R. E., The refractive index in electron optics and the principles of dynamics, Proceedings of the Physical Society, Section B 62 (1) (1949), 8–21, https://doi.org/10.1088/0370-1301/62/1/303.
  • Kato, T., On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jpn., 5 (6) (1950), 435–439, https://doi.org/10.1143/JPSJ.5.435.
  • Pancharatnam, S., Generalized theory of interference, and its applications, Proceedings of the Indian Academy of Sciences, Section A 44 (5) (1956), 247–262, https://doi.org/10.1007/BF03046050.
  • Longuet-Higgins, H. C., Opik, U., Pryce, M. H. L., Sack, R., Studies of the Jahn-Teller effect .II. The dynamical problem, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 244 (1236) (1958), 1–16, https://doi.org/10.1098/rspa.1958.0022.
  • Aharonov, Y., Bohm, D.: Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev., 115 (3) (1959), 485, https://doi.org/10.1103/PhysRev.115.485.
  • Berry, M. V., Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London A. Mathematical and Physical Sciences, 392 (1802) (1984), 45–57.
  • Aharonov, Y., Casher, A., Topological quantum effects for neutral particles, Phys. Rev. Lett., 53 (4) (1984), 319, https://doi.org/10.1103/PhysRevLett.53.319.
  • He, X.-G., McKellar, B. H. J., Topological phase due to electric dipole moment and magnetic monopole interaction, Phys. Rev. A, 47 (1993), 3424–3425, https://doi.org/10.1103/PhysRevA.47.3424.
  • Wilkens, M., Quantum phase of a moving dipole, Phys. Rev. Lett., 72 (1994), 5–8, https://doi.org/10.1103/PhysRevLett.72.5.
  • Dowling, J. P., Williams, C. P., Franson, J. D., Maxwell Duality, Lorentz invariance, and topological phase, Phys. Rev. Lett., 83 (1999), 2486–2489, https://doi.org/10.1103/PhysRevLett.83.2486.
  • Sponar, S., Klepp, J., Loidl, R., Filipp, S., Durstberger-Rennhofer, K., Bertlmann, R., Badurek, G., Rauch, H., Hasegawa, Y., Geometric phase in entangled systems: A single-neutron interferometer experiment, Phys. Rev. A, 81 (4) (2010), 042113, https://doi.org/10.1103/PhysRevA.81.042113.
  • Sponar, S., Klepp, J., Durstberger-Rennhofer, K., Loidl, R., Filipp, S., Lettner, M., Bertlmann, R., Badurek, G., Rauch, H., Hasegawa, Y., New aspects of geometric phases in experiments with polarized neutrons, J. Phys. A Math. Theor., 43 (35) (2010), 354015, https://doi.org/10.1088/1751-8113/43/35/354015.
  • Lepoutre, S., Gauguet, A., Trenec, G., Buchner, M., Vigue, J., He-McKellar-Wilkens topological phase in atom interferometry, Phys. Rev. Lett., 109 (12) (2012), 120404, https://doi.org/10.1103/PhysRevLett.109.120404.
  • Werner, S., Observation of Berry’s geometric phase by neutron interferometry, Found. Phys., 42 (1) (2012), 122–139, https://doi.org/10.1007/s10701-010-9526-z.
  • Gillot, J., Lepoutre, S., Gauguet, A., Buchner, M., Vigue, J., Measurement of the He-McKellar-Wilkens topological phase by atom interferometry and test of its independence with atom velocity, Phys. Rev. Lett., 111 (3) (2013), 030401, https://doi.org/10.1103/PhysRevLett.111.030401.
  • Cohen, E., Larocque, H., Bouchard, F., Nejadsattari, F., Gefen, Y., Karimi, E., Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond, Nat. Rev. Phys., 1 (7) (2019), 437–449, https://doi.org/10.1038/s42254-019-0071-1.
  • Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 47 (10) (1935), 777, https://doi.org/10.1103/PhysRev.47.777.
  • Bell, J. S., On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz., 1 (3) (1964), 195, https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195.
  • Clauser, J. F., Horne, M. A., Shimony, A., Holt, R. A., Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett., 23 (15) (1969), 880, https://doi.org/10.1103/PhysRevLett.23.880.
  • Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., Wootters, W. K., Mixed state entanglement and quantum error correction, Phys. Rev. A, 54 (5) (1996), 3824, https://doi.org/10.1103/PhysRevA.54.3824.
  • Wootters, W. K., Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80 (10) (1998), 2245, https://doi.org/10.1103/PhysRevLett.80.2245.
  • Werner, R. F., Entanglement Measures, Encyclopedia of Mathematical Physics, (2006), 233–236.
  • Plenio, M. B., Virmani, S., An Introduction to Entanglement Measures, Quantum Info. Comput., 7 (1) (2007), 1–51, https://doi.org/10.48550/arXiv.quant-ph/0504163.
  • Cildiroglu, H. O., 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.
  • Cirel’son, B. S., Quantum generalizations of Bell’s inequality, Lett. Math. Phys., 4 (2) (1980), 93–100.
  • Yuan, H., Fung, C.- H. F., Quantum parameter estimation with general dynamics, npj Quantum Information, 3 (14) (2017), 1–6.
  • Gisin, N.: Bell’s inequality holds for all non-product states, Phys. Lett. A, 154 (5) (1991), 201–202, https://doi.org/10.1016/0375-9601(91)90805-I.
  • Liang, Y.- C., Yeh, Y.- H., Mendonca, P. E., Teh, R. Y., Reid, M. D., Drummond, P. D., Quantum fidelity measures for mixed states, Rep. Prog. Phys., 82 (7) (2019), 076001, https://doi.org/10.1088/1361-6633/ab1ca4.
  • Kozlowski, W., Wehner, S., Meter, R.V., Rijsman, B., Cacciapuoti, A. S., Caleffi, M., Nagayama, S., Architectural Principles for a Quantum Internet, Internet Engineering Task Force. Work in Progress (2023), RFC 9340.
  • Jozsa, R., Fidelity for Mixed Quantum States, J. Mod. Opt., 41 (12) (1994), 2315–2323, https://doi.org/10.1080/09500349414552171.
  • Hubner, M., Explicit computation of the Bures distance for density matrices, Phys. Lett. A, 163 (4) (1992), 239–242, https://doi.org/10.1016/0375-9601(92)91004-B.
  • Bures, D., An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras, Trans. Am. Math. Soc., 135 (1969), 199–212.
  • Helstrom, C. W., Minimum mean-squared error of estimates in quantum statistics, Phys. Lett. A , 25 (2) (1967), 101–102, https://doi.org/10.1016/0375-9601(67)90366-0 .
  • Facchi, P., Kulkarni, R., Man’ko, V., Marmo, G., Sudarshan, E., Ventriglia, F., Classical and quantum Fisher information in the geometrical formulation of quantum mechanics, Phys. Lett. A, 374 (48) (2010), 4801–4803, https://doi.org/10.1016/j.physleta.2010.10.005.
  • Wootters, W. K., Statistical distance and Hilbert space, Phys. Rev. D, 23 (2) (1981), 357, https://doi.org/10.1103/PhysRevD.23.357.
  • Sandhya, S., Banerjee, S., Geometric phase: an indicator of entanglement, EPJ Plus D, 66 (6) (2012), 168, https://doi.org/10.1140/epjd/e2012-30211-5.
  • Vedral, V., Geometric phases and topological quantum computation, Int. J. Quantum Inf., 01 (01) (2003), 1–23, https://doi.org/10.48550/arXiv.quant-ph/0212133.
  • Sjoqvist, E., Geometric phases in quantum information, Int. J. Quantum Chem., 115 (19) (2015), 1311–1326, https://doi.org/10.1002/qua.2494.
  • Thomas, J., Geometric phase in quantum computation, (2016). Doctoral Thesis, George Mason University, United States.
  • Song, C., Zheng, S. -B., Zhang, P., Xu, K., Zhang, L., Guo, Q., Liu, W., Xu, D., Deng, H., Huang, K., Zheng, D., Zhu, X., Wang, H., Continuous variable geometric phase and its manipulation for quantum computation in a superconducting circuit, Nat. Commun., 8 (1) (2017), 1061, https://doi.org/10.1016/j.msea.2012.06.074.
  • Ji, L.- N., Ding, C.- Y., Chen, T., Xue, Z.- Y., Noncyclic geometric quantum gates with smooth paths via invariant-based shortcuts, Adv. Quantum Technol., 4 (6) (2021), 2100019, https://doi.org/10.1002/qute.202100019.
  • Zeilinger, A., General properties of lossless beam splitters in interferometry, Am. J. Phys., 49 (9) (1981), 882–883, https://doi.org/10.1119/1.12387.
  • Grangier, P., Roger, G., Aspect, A., Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences, EPL, 1 (4) (1986), 173–179, https://doi.org/10.1209/0295-5075/1/4/004.
  • Silverman, M. P., Quantum Superposition, Springer, Berlin, Heidelberg, 2008, 111–135

On the geometric phases in entangled states

Year 2023, Volume: 65 Issue: 2, 142 - 151, 29.12.2023

Melik Emirhan Tunalıoğlu , Hasan Özgür Çıldıroğlu , Ali Ulvi Yılmazer

https://doi.org/10.33769/aupse.1286632

Abstract

Correlation relations for the spin measurements on a pair of entangled particles scattered by the two separate arms of interferometers in hybrid setups of different types are investigated. Concurrence, entanglement of formation, quantum fidelity, Bures distance are used to clarify how the geometric phase affects the initial bipartite state. This affect causes a quantum interference due to the movement of charged particles in regions where electromagnetic fields are not present. We shown that in some cases the geometric phase information is carried over to the final bipartite entangled state.

Keywords

Geometric phase CHSH inequality concurrence entanglement of formation fidelity Bures distance

References

  • Ehrenberg, W., Siday, R. E., The refractive index in electron optics and the principles of dynamics, Proceedings of the Physical Society, Section B 62 (1) (1949), 8–21, https://doi.org/10.1088/0370-1301/62/1/303.
  • Kato, T., On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jpn., 5 (6) (1950), 435–439, https://doi.org/10.1143/JPSJ.5.435.
  • Pancharatnam, S., Generalized theory of interference, and its applications, Proceedings of the Indian Academy of Sciences, Section A 44 (5) (1956), 247–262, https://doi.org/10.1007/BF03046050.
  • Longuet-Higgins, H. C., Opik, U., Pryce, M. H. L., Sack, R., Studies of the Jahn-Teller effect .II. The dynamical problem, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 244 (1236) (1958), 1–16, https://doi.org/10.1098/rspa.1958.0022.
  • Aharonov, Y., Bohm, D.: Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev., 115 (3) (1959), 485, https://doi.org/10.1103/PhysRev.115.485.
  • Berry, M. V., Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London A. Mathematical and Physical Sciences, 392 (1802) (1984), 45–57.
  • Aharonov, Y., Casher, A., Topological quantum effects for neutral particles, Phys. Rev. Lett., 53 (4) (1984), 319, https://doi.org/10.1103/PhysRevLett.53.319.
  • He, X.-G., McKellar, B. H. J., Topological phase due to electric dipole moment and magnetic monopole interaction, Phys. Rev. A, 47 (1993), 3424–3425, https://doi.org/10.1103/PhysRevA.47.3424.
  • Wilkens, M., Quantum phase of a moving dipole, Phys. Rev. Lett., 72 (1994), 5–8, https://doi.org/10.1103/PhysRevLett.72.5.
  • Dowling, J. P., Williams, C. P., Franson, J. D., Maxwell Duality, Lorentz invariance, and topological phase, Phys. Rev. Lett., 83 (1999), 2486–2489, https://doi.org/10.1103/PhysRevLett.83.2486.
  • Sponar, S., Klepp, J., Loidl, R., Filipp, S., Durstberger-Rennhofer, K., Bertlmann, R., Badurek, G., Rauch, H., Hasegawa, Y., Geometric phase in entangled systems: A single-neutron interferometer experiment, Phys. Rev. A, 81 (4) (2010), 042113, https://doi.org/10.1103/PhysRevA.81.042113.
  • Sponar, S., Klepp, J., Durstberger-Rennhofer, K., Loidl, R., Filipp, S., Lettner, M., Bertlmann, R., Badurek, G., Rauch, H., Hasegawa, Y., New aspects of geometric phases in experiments with polarized neutrons, J. Phys. A Math. Theor., 43 (35) (2010), 354015, https://doi.org/10.1088/1751-8113/43/35/354015.
  • Lepoutre, S., Gauguet, A., Trenec, G., Buchner, M., Vigue, J., He-McKellar-Wilkens topological phase in atom interferometry, Phys. Rev. Lett., 109 (12) (2012), 120404, https://doi.org/10.1103/PhysRevLett.109.120404.
  • Werner, S., Observation of Berry’s geometric phase by neutron interferometry, Found. Phys., 42 (1) (2012), 122–139, https://doi.org/10.1007/s10701-010-9526-z.
  • Gillot, J., Lepoutre, S., Gauguet, A., Buchner, M., Vigue, J., Measurement of the He-McKellar-Wilkens topological phase by atom interferometry and test of its independence with atom velocity, Phys. Rev. Lett., 111 (3) (2013), 030401, https://doi.org/10.1103/PhysRevLett.111.030401.
  • Cohen, E., Larocque, H., Bouchard, F., Nejadsattari, F., Gefen, Y., Karimi, E., Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond, Nat. Rev. Phys., 1 (7) (2019), 437–449, https://doi.org/10.1038/s42254-019-0071-1.
  • Einstein, A., Podolsky, B., Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 47 (10) (1935), 777, https://doi.org/10.1103/PhysRev.47.777.
  • Bell, J. S., On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz., 1 (3) (1964), 195, https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195.
  • Clauser, J. F., Horne, M. A., Shimony, A., Holt, R. A., Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett., 23 (15) (1969), 880, https://doi.org/10.1103/PhysRevLett.23.880.
  • Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., Wootters, W. K., Mixed state entanglement and quantum error correction, Phys. Rev. A, 54 (5) (1996), 3824, https://doi.org/10.1103/PhysRevA.54.3824.
  • Wootters, W. K., Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80 (10) (1998), 2245, https://doi.org/10.1103/PhysRevLett.80.2245.
  • Werner, R. F., Entanglement Measures, Encyclopedia of Mathematical Physics, (2006), 233–236.
  • Plenio, M. B., Virmani, S., An Introduction to Entanglement Measures, Quantum Info. Comput., 7 (1) (2007), 1–51, https://doi.org/10.48550/arXiv.quant-ph/0504163.
  • Cildiroglu, H. O., 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.
  • Cirel’son, B. S., Quantum generalizations of Bell’s inequality, Lett. Math. Phys., 4 (2) (1980), 93–100.
  • Yuan, H., Fung, C.- H. F., Quantum parameter estimation with general dynamics, npj Quantum Information, 3 (14) (2017), 1–6.
  • Gisin, N.: Bell’s inequality holds for all non-product states, Phys. Lett. A, 154 (5) (1991), 201–202, https://doi.org/10.1016/0375-9601(91)90805-I.
  • Liang, Y.- C., Yeh, Y.- H., Mendonca, P. E., Teh, R. Y., Reid, M. D., Drummond, P. D., Quantum fidelity measures for mixed states, Rep. Prog. Phys., 82 (7) (2019), 076001, https://doi.org/10.1088/1361-6633/ab1ca4.
  • Kozlowski, W., Wehner, S., Meter, R.V., Rijsman, B., Cacciapuoti, A. S., Caleffi, M., Nagayama, S., Architectural Principles for a Quantum Internet, Internet Engineering Task Force. Work in Progress (2023), RFC 9340.
  • Jozsa, R., Fidelity for Mixed Quantum States, J. Mod. Opt., 41 (12) (1994), 2315–2323, https://doi.org/10.1080/09500349414552171.
  • Hubner, M., Explicit computation of the Bures distance for density matrices, Phys. Lett. A, 163 (4) (1992), 239–242, https://doi.org/10.1016/0375-9601(92)91004-B.
  • Bures, D., An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras, Trans. Am. Math. Soc., 135 (1969), 199–212.
  • Helstrom, C. W., Minimum mean-squared error of estimates in quantum statistics, Phys. Lett. A , 25 (2) (1967), 101–102, https://doi.org/10.1016/0375-9601(67)90366-0 .
  • Facchi, P., Kulkarni, R., Man’ko, V., Marmo, G., Sudarshan, E., Ventriglia, F., Classical and quantum Fisher information in the geometrical formulation of quantum mechanics, Phys. Lett. A, 374 (48) (2010), 4801–4803, https://doi.org/10.1016/j.physleta.2010.10.005.
  • Wootters, W. K., Statistical distance and Hilbert space, Phys. Rev. D, 23 (2) (1981), 357, https://doi.org/10.1103/PhysRevD.23.357.
  • Sandhya, S., Banerjee, S., Geometric phase: an indicator of entanglement, EPJ Plus D, 66 (6) (2012), 168, https://doi.org/10.1140/epjd/e2012-30211-5.
  • Vedral, V., Geometric phases and topological quantum computation, Int. J. Quantum Inf., 01 (01) (2003), 1–23, https://doi.org/10.48550/arXiv.quant-ph/0212133.
  • Sjoqvist, E., Geometric phases in quantum information, Int. J. Quantum Chem., 115 (19) (2015), 1311–1326, https://doi.org/10.1002/qua.2494.
  • Thomas, J., Geometric phase in quantum computation, (2016). Doctoral Thesis, George Mason University, United States.
  • Song, C., Zheng, S. -B., Zhang, P., Xu, K., Zhang, L., Guo, Q., Liu, W., Xu, D., Deng, H., Huang, K., Zheng, D., Zhu, X., Wang, H., Continuous variable geometric phase and its manipulation for quantum computation in a superconducting circuit, Nat. Commun., 8 (1) (2017), 1061, https://doi.org/10.1016/j.msea.2012.06.074.
  • Ji, L.- N., Ding, C.- Y., Chen, T., Xue, Z.- Y., Noncyclic geometric quantum gates with smooth paths via invariant-based shortcuts, Adv. Quantum Technol., 4 (6) (2021), 2100019, https://doi.org/10.1002/qute.202100019.
  • Zeilinger, A., General properties of lossless beam splitters in interferometry, Am. J. Phys., 49 (9) (1981), 882–883, https://doi.org/10.1119/1.12387.
  • Grangier, P., Roger, G., Aspect, A., Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences, EPL, 1 (4) (1986), 173–179, https://doi.org/10.1209/0295-5075/1/4/004.
  • Silverman, M. P., Quantum Superposition, Springer, Berlin, Heidelberg, 2008, 111–135
There are 44 citations in total.

Details

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

Melik Emirhan Tunalıoğlu 0000-0002-1143-9516

Hasan Özgür Çıldıroğlu 0000-0003-0246-1102

Ali Ulvi Yılmazer This is me 0000-0002-2270-8486

Early Pub Date October 7, 2023
Publication Date December 29, 2023
Submission Date April 23, 2023
Acceptance Date June 8, 2023
Published in Issue Year 2023 Volume: 65 Issue: 2

Cite

APA Tunalıoğlu, M. E., Çıldıroğlu, H. Ö., & Yılmazer, A. U. (2023). On the geometric phases in entangled states. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, 65(2), 142-151. https://doi.org/10.33769/aupse.1286632
AMA Tunalıoğlu ME, Çıldıroğlu HÖ, Yılmazer AU. On the geometric phases in entangled states. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. December 2023;65(2):142-151. doi:10.33769/aupse.1286632
Chicago Tunalıoğlu, Melik Emirhan, Hasan Özgür Çıldıroğlu, and Ali Ulvi Yılmazer. “On the Geometric Phases in Entangled States”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 65, no. 2 (December 2023): 142-51. https://doi.org/10.33769/aupse.1286632.
EndNote Tunalıoğlu ME, Çıldıroğlu HÖ, Yılmazer AU (December 1, 2023) On the geometric phases in entangled states. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 65 2 142–151.
IEEE M. E. Tunalıoğlu, H. Ö. Çıldıroğlu, and A. U. Yılmazer, “On the geometric phases in entangled states”, Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng., vol. 65, no. 2, pp. 142–151, 2023, doi: 10.33769/aupse.1286632.
ISNAD Tunalıoğlu, Melik Emirhan et al. “On the Geometric Phases in Entangled States”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 65/2 (December 2023), 142-151. https://doi.org/10.33769/aupse.1286632.
JAMA Tunalıoğlu ME, Çıldıroğlu HÖ, Yılmazer AU. On the geometric phases in entangled states. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2023;65:142–151.
MLA Tunalıoğlu, Melik Emirhan et al. “On the Geometric Phases in Entangled States”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, vol. 65, no. 2, 2023, pp. 142-51, doi:10.33769/aupse.1286632.
Vancouver Tunalıoğlu ME, Çıldıroğlu HÖ, Yılmazer AU. On the geometric phases in entangled states. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2023;65(2):142-51.

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.