Yıl: 2023 Cilt: 65 Sayı: 2 Sayfa Aralığı: 142 - 151 Metin Dili: İngilizce DOI: 10.33769/aupse.1286632 İndeks Tarihi: 07-11-2023

ON THE GEOMETRIC PHASES IN ENTANGLED STATES

Öz:
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.
Anahtar Kelime: Geometric phase CHSH inequality concurrence entanglement of formation fidelity Bures distance

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Ehrenberg, W., Siday, R. E., The refractive index in electron optics and the princi- ples of dynamics, Proceedings of the Physical Society, Section B 62 (1) (1949), 8–21, https://doi.org/10.1088/0370-1301/62/1/303.
  • [2] 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.
  • [3] Pancharatnam, S., Generalized theory of interference, and its applications, Pro- ceedings of the Indian Academy of Sciences, Section A 44 (5) (1956), 247–262, https://doi.org/10.1007/BF03046050.
  • [4] 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. Mathemat- ical and Physical Sciences, 244 (1236) (1958), 1–16, https://doi.org/10.1098/rspa.1958.0022.
  • [5] 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.
  • [6] 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.
  • [7] 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.
  • [8] He, X. -G., McKellar, B. H. J., Topological phase due to electric dipole mo- ment and magnetic monopole interaction, Phys. Rev. A, 47 (1993), 3424–3425, https://doi.org/10.1103/PhysRevA.47.3424.
  • [9] Wilkens, M., Quantum phase of a moving dipole, Phys. Rev. Lett., 72 (1994), 5–8, https://doi.org/10.1103/PhysRevLett.72.5.
  • [10] 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.
  • [11] 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.
  • [12] Sponar, S., Klepp, J., Durstberger-Rennhofer, K., Loidl, R., Filipp, S., Lettner, M., Bertl- mann, 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.
  • [13] 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.
  • [14] 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.
  • [15] 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.
  • [16] 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.
  • [17] 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.
  • [18] Bell, J. S., On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz., 1 (3) (1964), 195, https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195.
  • [19] Clauser, J. F., Horne, M. A., Shimony, A., Holt, R. A., Proposed experi- ment to test local hidden-variable theories, Phys. Rev. Lett., 23 (15) (1969), 880, https://doi.org/10.1103/PhysRevLett.23.880.
  • [20] 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.
  • [21] 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.
  • [22] Werner, R. F., Entanglement Measures, Encyclopedia of Mathematical Physics, (2006), 233–236.
  • [23] 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.
  • [24] 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.
  • [25] Cirel’son, B. S., Quantum generalizations of Bell’s inequality, Lett. Math. Phys., 4 (2) (1980), 93–100.
  • [26] Yuan, H., Fung, C.- H. F., Quantum parameter estimation with general dynamics, npj Quan- tum Information, 3 (14) (2017), 1–6.
  • [27] 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.
  • [28] 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.
  • [29] Kozlowski, W., Wehner, S., Meter, R.V., Rijsman, B., Cacciapuoti, A. S., Caleffi, M., Na- gayama, S., Architectural Principles for a Quantum Internet, Internet Engineering Task Force. Work in Progress (2023), RFC 9340.
  • [30] Jozsa, R., Fidelity for Mixed Quantum States, J. Mod. Opt., 41 (12) (1994), 2315–2323, https://doi.org/10.1080/09500349414552171.
  • [31] 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.
  • [32] 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.
  • [33] 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 .
  • [34] 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.
  • [35] Wootters, W. K., Statistical distance and Hilbert space, Phys. Rev. D, 23 (2) (1981), 357, https://doi.org/10.1103/PhysRevD.23.357.
  • [36] 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.
  • [37] 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.
  • [38] Sjoqvist, E., Geometric phases in quantum information, Int. J. Quantum Chem., 115 (19) (2015), 1311–1326, https://doi.org/10.1002/qua.2494.
  • [39] Thomas, J., Geometric phase in quantum computation, (2016). Doctoral Thesis, George Mason University, United States.
  • [40] 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.
  • [41] 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.
  • [42] 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.
  • [43] 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.
  • [44] Silverman, M. P., Quantum Superposition, Springer, Berlin, Heidelberg, 2008, 111–135.
APA Tunalıoğlu M, ÇILDIROĞLU H, YILMAZER A (2023). ON THE GEOMETRIC PHASES IN ENTANGLED STATES. , 142 - 151. 10.33769/aupse.1286632
Chicago Tunalıoğlu Melik Emirhan,ÇILDIROĞLU HASAN ÖZGÜR,YILMAZER Ali Ulvi ON THE GEOMETRIC PHASES IN ENTANGLED STATES. (2023): 142 - 151. 10.33769/aupse.1286632
MLA Tunalıoğlu Melik Emirhan,ÇILDIROĞLU HASAN ÖZGÜR,YILMAZER Ali Ulvi ON THE GEOMETRIC PHASES IN ENTANGLED STATES. , 2023, ss.142 - 151. 10.33769/aupse.1286632
AMA Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A ON THE GEOMETRIC PHASES IN ENTANGLED STATES. . 2023; 142 - 151. 10.33769/aupse.1286632
Vancouver Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A ON THE GEOMETRIC PHASES IN ENTANGLED STATES. . 2023; 142 - 151. 10.33769/aupse.1286632
IEEE Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A "ON THE GEOMETRIC PHASES IN ENTANGLED STATES." , ss.142 - 151, 2023. 10.33769/aupse.1286632
ISNAD Tunalıoğlu, Melik Emirhan vd. "ON THE GEOMETRIC PHASES IN ENTANGLED STATES". (2023), 142-151. https://doi.org/10.33769/aupse.1286632
APA Tunalıoğlu M, ÇILDIROĞLU H, YILMAZER A (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. 10.33769/aupse.1286632
Chicago Tunalıoğlu Melik Emirhan,ÇILDIROĞLU HASAN ÖZGÜR,YILMAZER Ali Ulvi ON THE GEOMETRIC PHASES IN ENTANGLED STATES. Communications Faculty of Sciences University of Ankara Series A2-A3: Physical Sciences and Engineering 65, no.2 (2023): 142 - 151. 10.33769/aupse.1286632
MLA Tunalıoğlu Melik Emirhan,ÇILDIROĞLU HASAN ÖZGÜR,YILMAZER Ali Ulvi 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, ss.142 - 151. 10.33769/aupse.1286632
AMA Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A ON THE GEOMETRIC PHASES IN ENTANGLED STATES. Communications Faculty of Sciences University of Ankara Series A2-A3: Physical Sciences and Engineering. 2023; 65(2): 142 - 151. 10.33769/aupse.1286632
Vancouver Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A ON THE GEOMETRIC PHASES IN ENTANGLED STATES. Communications Faculty of Sciences University of Ankara Series A2-A3: Physical Sciences and Engineering. 2023; 65(2): 142 - 151. 10.33769/aupse.1286632
IEEE Tunalıoğlu M,ÇILDIROĞLU H,YILMAZER A "ON THE GEOMETRIC PHASES IN ENTANGLED STATES." Communications Faculty of Sciences University of Ankara Series A2-A3: Physical Sciences and Engineering, 65, ss.142 - 151, 2023. 10.33769/aupse.1286632
ISNAD Tunalıoğlu, Melik Emirhan vd. "ON THE GEOMETRIC PHASES IN ENTANGLED STATES". Communications Faculty of Sciences University of Ankara Series A2-A3: Physical Sciences and Engineering 65/2 (2023), 142-151. https://doi.org/10.33769/aupse.1286632