Skip to main content
SpringerLink
Log in

Open system approach to neutrino oscillations in a quantum walk framework

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum simulation provides a computationally feasible approach to model and study many problems in chemistry, condensed-matter physics, or high-energy physics where quantum phenomenon defines the systems behavior. In high-energy physics, quite a few possible applications are investigated in the context of gauge theories and their application to dynamic problems, topological problems, high-baryon density configurations, or collective neutrino oscillations. In particular, schemes for simulating neutrino oscillations are proposed using a quantum walk framework. In this study, we approach the problem of simulating neutrino oscillation from the perspective of open quantum systems by treating the position space of quantum walk as environment. We have obtained the recurrence relation for Kraus operator which is used to represent the dynamics of the neutrino flavor change in the form of reduced coin states. We establish a connection between the dynamics of reduced coin state and neutrino phenomenology, enabling one to fix the simulation parameters for a given neutrino experiment and reduces the need for extended position space to simulate neutrino oscillations. We have also studied the behavior of linear entropy as a measure of entanglement between different flavors in the same framework.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86, 153 (2014). https://doi.org/10.1103/RevModPhys.86.153

    Article  ADS  Google Scholar 

  2. Browaeys, A., Lahaye, T.: Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132 (2020). https://doi.org/10.1038/s41567-019-0733-z

    Article  Google Scholar 

  3. Hartmann, M.J.: Quantum simulation with interacting photons. J. Opt. 18, 104005 (2016). https://doi.org/10.1088/2040-8978/18/10/104005

    Article  ADS  Google Scholar 

  4. Houck, A.A., Türeci, H.E., Koch, J.: On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292 (2012). https://doi.org/10.1038/nphys2251

    Article  Google Scholar 

  5. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T.W., et al.: Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39 (2002). https://doi.org/10.1038/415039a

    Article  ADS  Google Scholar 

  6. Blatt, R., Roos, C.F.: Quantum simulations with trapped ions. Nat. Phys. 8, 277 (2012). https://doi.org/10.1038/nphys2252

    Article  Google Scholar 

  7. Monroe, C., Campbell, W., Duan, L.M., Gong, Z.X., et al.: Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021). https://doi.org/10.1103/RevModPhys.93.025001

    Article  ADS  MathSciNet  Google Scholar 

  8. Aspuru-Guzik, A., Walther, P.: Photonic quantum simulators. Nat. Phys. 8, 285 (2012). https://doi.org/10.1038/nphys2253

    Article  Google Scholar 

  9. Gross, C., Bloch, I.: Quantum simulations with ultracold atoms in optical lattices. Science 357, 995 (2017). https://doi.org/10.1126/science.aal3837

    Article  ADS  Google Scholar 

  10. White, A.G.: Conference on Lasers and Electro-Optics, Conference on Lasers and Electro-Optics, FTh4C.1 (2016). https://doi.org/10.1364/CLEO_QELS.2016.FTh4C.1

  11. Cirac, J.I., Zoller, P.: Goals and opportunities in quantum simulation. Nat. Phys. 8, 264 (2012). https://doi.org/10.1038/nphys2275

    Article  Google Scholar 

  12. Daley, A.J., Bloch, I., Kokail, C., Flannigan, S., Pearson, N., et al.: Practical quantum advantage in quantum simulation. Nature 607, 667 (2022). https://doi.org/10.1038/s41586-022-04940-6

    Article  ADS  Google Scholar 

  13. Verstraete, F., Porras, D., Cirac, J.I.: Practical quantum advantage in quantum simulation. Phys. Rev. Lett. 93, 227205 (2004). https://doi.org/10.1103/PhysRevLett.93.227205

    Article  ADS  Google Scholar 

  14. Nalewajski, R.F.: Understanding electronic structure and chemical reactivity: quantum-information perspective. Appl. Sci. 9, 1262 (2019). https://doi.org/10.3390/app9061262

    Article  Google Scholar 

  15. Wasielewski, M.R., Forbes, M.D.E., Frank, N.L., Kowalski, K., et al.: Exploiting chemistry and molecular systems for quantum information science. Nat. Rev. Chem. 4, 490 (2020). https://doi.org/10.1038/s41570-020-0200-5

    Article  Google Scholar 

  16. Lewis-Swan, R.J., Safavi-Naini, A., Kaufman, A.M., Rey, A.M.: Dynamics of quantum information. Nat. Rev. Phys. 1, 627 (2019). https://doi.org/10.1038/s42254-019-0090-y

    Article  Google Scholar 

  17. Augusiak, R., Cucchietti, F.M., Lewenstein, M.: Many Body Physics from a Quantum Information. Perspective (2012). https://doi.org/10.1007/978-3-642-10449-7_6

    Article  Google Scholar 

  18. Goold, J., Huber, M., Riera, A., Rio, L.D., Skrzypczyk, P.: The role of quantum information in thermodynamics’a topical review. J. Phys. A Math. Theor. 49, 143001 (2016). https://doi.org/10.1088/1751-8113/49/14/143001

    Article  ADS  MathSciNet  Google Scholar 

  19. Lloyd, S.: Quantum information. Matters Sci. 319, 1209 (2008). https://doi.org/10.1126/science.1154732

    Article  Google Scholar 

  20. Venegas-Andraca, S.E.: Quantum walks: a comprehensive review. Quantum Inf. Process. 11, 1015 (2012). https://doi.org/10.1007/s11128-012-0432-5

    Article  MathSciNet  Google Scholar 

  21. Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., et.al.: One-dimensional quantum walks. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. 37–49. Association for Computing Machinery (2001). https://doi.org/10.1145/380752.380757

  22. Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.: Quantum walks on graphs. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, Association for Computing Machinery Bibinfo Series STOC’01, pp. 50–59 (2001). https://doi.org/10.1145/380752.380758

  23. Venegas-Andraca, S.: Quantum walks and their algorithmic applications. Int. J. Quantum Inf. 2, 365 (2004)

    Google Scholar 

  24. Oka, T., Konno, N., Arita, R., Aoki, H.: Breakdown of an electric-field driven system: a mapping to a quantum walk. Phys. Rev. Lett. 94, 100602 (2005). https://doi.org/10.1103/PhysRevLett.94.100602

    Article  ADS  Google Scholar 

  25. Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T.-K., et al.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782 (2007). https://doi.org/10.1038/nature05678

    Article  ADS  Google Scholar 

  26. Mohseni, M., Rebentrost, P., Lloyd, S., Aspuru-Guzik, A.: Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008). https://doi.org/10.1063/1.3002335

    Article  ADS  Google Scholar 

  27. Chandrashekar, C.M., Laflamme, R.: Quantum phase transition using quantum walks in an optical lattice. Phys. Rev. A 78, 022314 (2008). https://doi.org/10.1103/PhysRevA.78.022314

    Article  ADS  Google Scholar 

  28. Chandrashekar, C.M.: Disordered-quantum-walk-induced localization of a Bose-Einstein condensate. Phys. Rev. A 83, 022320 (2011). https://doi.org/10.1103/PhysRevA.83.022320

    Article  ADS  Google Scholar 

  29. Kitagawa, T., Rudner, M.S., Berg, E., Demler, E.: Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010). https://doi.org/10.1103/PhysRevA.82.033429

    Article  ADS  Google Scholar 

  30. Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003). https://doi.org/10.1103/PhysRevA.67.052307

    Article  ADS  Google Scholar 

  31. Childs, A.M., Cleve, R., Deotto, E., Farhi, E., et.al.: Exponential algorithmic speedup by a quantum walk. In: Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing, vol. 59 (2003). https://doi.org/10.1145/780542.780552

  32. Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, p. 1099 (2005)

  33. Chandrashekar, C.M:. Discrete-Time Quantum Walk—Dynamics and Applications Discrete-Time Quantum Walk—Dynamics and Applications (2010), arXiv:1001.5326 [quant-ph]. https://doi.org/10.48550/arXiv.1001.5326

  34. Mülken, O., Blumen, A.: Continuous-time quantum walks: models for coherent transport on complex networks. Phys. Rep. 502, 37 (2011). https://doi.org/10.1016/j.physrep.2011.01.002

    Article  ADS  MathSciNet  Google Scholar 

  35. Flurin, E., Ramasesh, V., Hacohen-Gourgy, S., Martin, L., Yao, N., Siddiqi, I.: Observing topological invariants using quantum walks in superconducting circuits. Phys. Rev. X 7, 031023 (2017). https://doi.org/10.1103/PhysRevX.7.031023

    Article  Google Scholar 

  36. Ramasesh, V., Flurin, E., Rudner, M., et al.: Direct probe of topological invariants using bloch oscillating quantum walks. Phys. Rev. Lett. 118, 130501 (2017). https://doi.org/10.1103/PhysRevLett.118.130501

    Article  ADS  MathSciNet  Google Scholar 

  37. Qiang, X., Loke, T., Montanaro, A., et al.: Efficient quantum walk on a quantum processor. Nat. Commun. 7, 11511 (2016). https://doi.org/10.1038/ncomms11511

    Article  ADS  Google Scholar 

  38. Peruzzo, A., Lobino, M., Matthews, J.C.F., et al.: Quantum walks of correlated photons. Science 329, 1500 (2010). https://doi.org/10.1126/science.1193515

    Article  ADS  Google Scholar 

  39. Tamura, M., Mukaiyama, T., Toyoda, K.: Quantum walks of a phonon in trapped ions. Phys. Rev. Lett. 124, 200501 (2020). https://doi.org/10.1103/PhysRevLett.124.200501

    Article  ADS  Google Scholar 

  40. Karski, M., Förster, L., Choi, J.M., et al.: Quantum walk in position space with single optically trapped atoms. Science 325, 174 (2009). https://doi.org/10.1126/science.1174436

    Article  ADS  Google Scholar 

  41. Broome, M.A., Fedrizzi, A., Lanyon, B.P., et al.: Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010). https://doi.org/10.1103/PhysRevLett.104.153602

    Article  ADS  Google Scholar 

  42. Perets, H.B., Lahini, Y., Pozzi, F., Sorel, M., et al.: Realization of quantum walks with negligible decoherence in waveguide lattices. Phys. Rev. Lett. 100, 170506 (2008). https://doi.org/10.1103/PhysRevLett.100.170506

    Article  ADS  Google Scholar 

  43. Zähringer, F., Kirchmair, G., Gerritsma, R., Solano, E., et al.: Realization of a quantum walk with one and two trapped ions. Phys. Rev. Lett. 104, 100503 (2010). https://doi.org/10.1103/PhysRevLett.104.100503

    Article  ADS  Google Scholar 

  44. Ryan, C.A., Laforest, M., Boileau, J.C., Laflamme, R.: Experimental implementation of a discrete-time quantum random walk on an NMR quantum-information processor. Phys. Rev. A 72, 062317 (2005). https://doi.org/10.1103/PhysRevA.72.062317

    Article  ADS  Google Scholar 

  45. Schreiber, A., Cassemiro, K.N., Potoek, V., Gábris, A., et al.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010). https://doi.org/10.1103/PhysRevLett.104.050502

    Article  ADS  Google Scholar 

  46. Chandrashekar, C.M.: Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices. Sci. Rep. 3, 2829 (2013). https://doi.org/10.1038/srep02829

    Article  ADS  Google Scholar 

  47. Mallick, A., Chandrashekar, C.M.: Dirac cellular automaton from split-step quantum walk. Sci. Rep. 6, 25779 (2016). https://doi.org/10.1038/srep25779

    Article  ADS  Google Scholar 

  48. Mallick, A., Mandal, S., Karan, A., Chandrashekar, C.M.: Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk. J. Phys. Commun. 3, 015012 (2019). https://doi.org/10.1088/2399-6528/aafe2f

    Article  Google Scholar 

  49. Strauch, F.W.: Relativistic quantum walks. Phys. Rev. A 73, 054302 (2006). https://doi.org/10.1103/PhysRevA.73.054302

    Article  ADS  MathSciNet  Google Scholar 

  50. Huerta Alderete, C., Singh, S., Nguyen, N.H., et al.: Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer. Nat. Commun. 11, 3720 (2020). https://doi.org/10.1038/s41467-020-17519-4

    Article  ADS  Google Scholar 

  51. Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., Roos, C.F.: Quantum simulation of the Dirac equation. Nature 463, 68 (2010). https://doi.org/10.1038/nature08688

    Article  ADS  Google Scholar 

  52. Qu, C., Hamner, C., Gong, M., Zhang, C., Engels, P.: Observation of Zitterbewegung in a spin-orbit-coupled Bose-Einstein condensate. Phys. Rev. A 88, 021604 (2013). https://doi.org/10.1103/PhysRevA.88.021604

    Article  ADS  Google Scholar 

  53. Lovett, S., Walker, P.M., Osipov, A., Yulin, A., Naik, P.U., Whittaker, C.E., Shelykh, I.A., Skolnick, M.S., Krizhanovskii, D.N.: Observation of Zitterbewegung in photonic microcavities Observation of Zitterbewegung in photonic microcavities (2023), arXiv:2211.09907 [cond-mat, physics:physics]. https://doi.org/10.48550/arXiv.2211.09907

  54. Liu, T., Feng, M., Yang, W., Chen, L., Zhou, F., Wang, K.: Quantum simulation of ‘zitterbewegung’ in a single trapped ion under conditions of parity-keeping and parity-breaking. Sci. China Phys. Mech. Astron. 57, 1250 (2014). https://doi.org/10.1007/s11433-014-5458-5

    Article  ADS  Google Scholar 

  55. Brun, T.A., Mlodinow, L.: Quantum cellular automata and quantum field theory in two spatial dimensions. Phys. Rev. A 102, 062222 (2020). https://doi.org/10.1103/PhysRevA.102.062222

    Article  ADS  MathSciNet  Google Scholar 

  56. Arnault, P., Di Molfetta, G., Brachet, M., Debbasch, F.: Quantum walks and non-Abelian discrete gauge theory. Phys. Rev. A 94, 012335 (2016). https://doi.org/10.1103/PhysRevA.94.012335

    Article  ADS  MathSciNet  Google Scholar 

  57. Arrighi, P., Facchini, S., Forets, M.: Quantum walking in curved spacetime. Quantum Inf. Process. 15, 3467 (2016). https://doi.org/10.1007/s11128-016-1335-7

    Article  ADS  MathSciNet  Google Scholar 

  58. Arnault, P., Pérez, A., Arrighi, P., Farrelly, T.: Discrete-time quantum walks as fermions of lattice gauge theory. Phys. Rev. A 99, 032110 (2019). https://doi.org/10.1103/PhysRevA.99.032110

    Article  ADS  Google Scholar 

  59. Hall, B., Roggero, A., Baroni, A., Carlson, J.: Simulation of collective neutrino oscillations on a quantum computer. Phys. Rev. D 104, 063009 (2021). https://doi.org/10.1103/PhysRevD.104.063009

    Article  ADS  Google Scholar 

  60. Lesgourgues, J., Pastor, S.: Neutrino cosmology and Planck. New J. Phys. 16, 065002 (2014). https://doi.org/10.1088/1367-2630/16/6/065002

    Article  ADS  Google Scholar 

  61. Qian, X., Peng, J.C.: Physics with reactor neutrinos. Rep. Prog. Phys. 82, 036201 (2019). https://doi.org/10.1088/1361-6633/aae881

    Article  ADS  Google Scholar 

  62. Hayes, A.C., Vogel, P.: Reactor neutrino spectra. Annu. Rev. Nucl. Part. Sci. 66, 219 (2016). https://doi.org/10.1146/annurev-nucl-102115-044826

    Article  ADS  Google Scholar 

  63. Duan, H., Fuller, G.M., Qian, Y.-Z.: Collective neutrino oscillations. Annu. Rev. Nucl. Part. Sci. 60, 569 (2010). https://doi.org/10.1146/annurev.nucl.012809.104524

    Article  ADS  Google Scholar 

  64. Mirizzi, A., Tamborra, I., Janka, H.T., Saviano., K. Scholberg, R. Bollig, L., Hüdepohl, S. Chakraborty,: Supernova neutrinos: production, oscillations and detection. La Rivista del Nuovo Cimento 39, 1 (2016). https://doi.org/10.1393/ncr/i2016-10120-8

  65. Bahcall, J.N., Peña-Garay, C.: Solar models and solar neutrino oscillations. New J. Phys. 6, 63 (2004). https://doi.org/10.1088/1367-2630/6/1/063

    Article  ADS  Google Scholar 

  66. Gonzalez-Garcia, M.C., Maltoni, M.: Phenomenology with massive neutrinos. Phys. Rep. 460, 1 (2008). https://doi.org/10.1016/j.physrep.2007.12.004

    Article  ADS  Google Scholar 

  67. Mallick, A., Mandal, S., Chandrashekar, C.M.: Neutrino oscillations in discrete-time quantum walk framework. Eur. Phys. J. C 77, 85 (2017). https://doi.org/10.1140/epjc/s10052-017-4636-9

    Article  ADS  Google Scholar 

  68. Molfetta, G.D., Pérez, A.: Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys. 18, 103038 (2016). https://doi.org/10.1088/1367-2630/18/10/103038

    Article  Google Scholar 

  69. Banerjee, S., Alok, A.K., Srikanth, R., Hiesmayr, B.C.: A quantum-information theoretic analysis of three-flavor neutrino oscillations. Eur. Phys. J. C 75, 487 (2015). https://doi.org/10.1140/epjc/s10052-015-3717-x

    Article  ADS  Google Scholar 

  70. Kajita, T., Totsuka, Y.: Observation of atmospheric neutrinos. Rev. Mod. Phys. 73, 85 (2001). https://doi.org/10.1103/RevModPhys.73.85

    Article  ADS  Google Scholar 

  71. Davis, R., Harmer, D.S., Hoffman, K.C.: Search for neutrinos from the Sun. Phys. Rev. Lett. 20, 1205 (1968). https://doi.org/10.1103/PhysRevLett.20.1205

    Article  ADS  Google Scholar 

  72. Gonzalez-Garcia, M.C., Maltoni, M.: Phenomenology with massive neutrinos. Phys. Rep. 460, 1 (2008). https://doi.org/10.1016/j.physrep.2007.12.004

    Article  ADS  Google Scholar 

  73. Bilenky, S.M., Petcov, S.T.: Massive neutrinos and neutrino oscillations. Rev. Mod. Phys. 59, 671 (1987). https://doi.org/10.1103/RevModPhys.59.671

    Article  ADS  Google Scholar 

  74. Bilenky, S.M., Pontecorvo, B.: Lepton mixing and neutrino oscillations. Phys. Rep. 41, 225 (1978). https://doi.org/10.1016/0370-1573(78)90095-9

    Article  ADS  Google Scholar 

  75. Bilenky, S.: Neutrino oscillations: from an historical perspective to the present status. J. Phys. Conf. Ser. 718, 062005 (2016). https://doi.org/10.1088/1742-6596/718/6/062005

    Article  MathSciNet  Google Scholar 

  76. Maki, Z., Nakagawa, M., Sakata, S.: Remarks on the unified model of elementary particles. Prog. Theor. Phys. 28, 870 (1962). https://doi.org/10.1143/PTP.28.870

    Article  ADS  Google Scholar 

  77. Kajita, T.: Nobel lecture: discovery of atmospheric neutrino oscillations. Rev. Mod. Phys. 88, 030501 (2016). https://doi.org/10.1103/RevModPhys.88.030501

    Article  ADS  Google Scholar 

  78. Fukuda, S., Fukuda, Y., Ishitsuka, M., Itow, Y., et al.: Determination of solar neutrino oscillation parameters using 1496 days of Super-Kamiokande-I data. Phys. Lett. B 539, 179 (2002). https://doi.org/10.1016/S0370-2693(02)02090-7

    Article  ADS  Google Scholar 

  79. Naikoo, J., Banerjee, S., Chandrashekar, C.M.: Non-Markovian channel from the reduced dynamics of a coin in a quantum walk. Phys. Rev. A 102, 062209 (2020). https://doi.org/10.1103/PhysRevA.102.062209

    Article  ADS  MathSciNet  Google Scholar 

  80. Wikipedia: Neutrino oscillation. http://en.wikipedia.org/w/index.php?title=Neutrino%20oscillation &oldid=1143844099. Neutrino oscillation (2023)

  81. Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008). https://doi.org/10.1103/RevModPhys.80.517

    Article  ADS  MathSciNet  Google Scholar 

  82. Blasone, M., Dell’Anno, F., Siena, S.D., Illuminati, F.: Entanglement in neutrino oscillations. Europhys. Lett. 85, 50002 (2009). https://doi.org/10.1209/0295-5075/85/50002

    Article  ADS  Google Scholar 

  83. Hu, Z., Xia, R., Kais, S.: A quantum algorithm for evolving open quantum dynamics on quantum computing devices. Sci. Rep. 10, 1 (2020). https://doi.org/10.1038/s41598-020-60321-x

    Article  Google Scholar 

  84. Hu, Z., Head-Marsden, K., Mazziotti, D.A., Narang, P., Kais, S.: A general quantum algorithm for open quantum dynamics demonstrated with the Fenna–Matthews–Olson complex. Quantum 6, 726 (2022). https://doi.org/10.22331/q-2022-05-30-726

  85. Benatti, F., Floreanini, R.: Open system approach to neutrino oscillations. J. High Energy Phys. 2000, 032 (2000). https://doi.org/10.1088/1126-6708/2000/02/032

    Article  Google Scholar 

  86. Lisi, E., Marrone, A., Montanino, D.: Probing possible decoherence effects in atmospheric neutrino oscillations. Phys. Rev. Lett. 85, 1166 (2000). https://doi.org/10.1103/PhysRevLett.85.1166

    Article  ADS  Google Scholar 

  87. Gomes, G.B., Forero, D.V., Guzzo, M.M., de Holanda, P.C., Oliveira, R.L.N.: Quantum decoherence effects in neutrino oscillations at DUNE. Phys. Rev. D 100, 055023 (2019). https://doi.org/10.1103/PhysRevD.100.055023

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank Mr. Prateek Chawla for his comments on the manuscript.

Author information

Authors and Affiliations

  1. Department of Instrumentation and Applied Physics, Indian Institute of Sciences, C.V. Raman Avenue, Bengaluru, 560012, India

    Himanshu Sahu & C. M. Chandrashekar

  2. The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai, 600113, India

    C. M. Chandrashekar

  3. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India

    C. M. Chandrashekar

Authors
  1. Himanshu Sahu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. M. Chandrashekar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.M.C. and H.S. wrote the main manuscript text and H.S. prepared all figures. All authors reviewed the manuscript.

Corresponding author

Correspondence to Himanshu Sahu.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahu, H., Chandrashekar, C.M. Open system approach to neutrino oscillations in a quantum walk framework. Quantum Inf Process 23, 7 (2024). https://doi.org/10.1007/s11128-023-04222-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04222-8

Keywords

Search

Navigation