Asian Journal of Physics Vol. 33, No 11 (2024) 667-681

Quantum chaos and macroscopic realism as no-signaling in time

Manish Ramchander1
Institute of Mathematical Sciences, Taramani, Chennai-60 0113, India.

Arul Lakshminarayan2
Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India

Macroscopic realism is a set of assumptions about how we experience the world at a classical level. While the Leggett-Garg inequalities are temporal correlations that are violated by quantum systems not obeying such macrorealism, the no-signaling in time condition is also a necessary condition. This compares measurement outcomes with and without prior measurements. As dynamics and correlations play a central role in these measures, this paper explores the effects of regular versus chaotic dynamics on the violations of macroscopic realism. We observe a close connection between a 3 point out-of-time-order correlator and the conditional probabilities of measurement, and we find unmistakable imprints of chaos on the violations of macrorealism. We provide qualitative semiclassical reasoning for the numerical results involving a kicked top, and for two important initial states that behave very differently. © Anita Publications. All rights reserved.
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Keywords: Macrorealism, Leggett-Garg inequalities, Quantum chaos

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References

  1. Leggett A J, Garg A, Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?, Phys Rev Lett, 54(1985)857–860.
  2. Leggett A J, Testing the limits of quantummechanics: motivation, state of play, prospects, J Phys: Condens Matter, 14(2002)R415; doi. 10.1088/0953-8984/14/15/201.
  3. Kofler J, Brukner Č, Condition for macroscopic realism beyond the Leggett-Garg inequalities, Phys Rev A, 87(2013)052115; doi. doi.org/10.1103/PhysRevA.87.052115.
  4. Emary C, Lambert N, Nori F, Leggett–garg inequalities, Rep Prog Phys, 77(2013)016001; doi.10.1088/0034-4885/77/1/016001.
  5. Clemente L, Kofler J, Necessary and sufficient conditions for macroscopic realism fromquantummechanics, Phys Rev A, 91(2015)062103; doi.org/10.1103/PhysRevA.91.062103.
  6. Clemente L, Kofler J, No fine theorem for macrorealism: Limitations of the Leggett-Garg inequality, Phys Rev Lett, 116(2016)150401; doi.org/10.1103/PhysRevLett.116.150401.
  7. Halliwell J J, Comparing conditions for macrorealism: Leggett-Garg inequalities versus no-signaling in time, Phys Rev A, 96(2017)012121; doi. doi.org/10.1103/PhysRevA.96.012121.
  8. D’Alessio L, Kafri Y, Polkovnikov A, Rigol M, Adv Phys, 65(2016)239; org/10.1080/00018732.2016.1198134.
  9. Strasberg P, Reinhard T E, Schindler J, First principles numerical demonstration of emergent decoherent histories Phys Rev X, 14(2024)041027;doi.org/10.1103/PhysRevX.14.041027.
  10. Fröwis F, Sekatski P, Dür W, Gisin N, Sangouard N, Macroscopic quantum states: Measures, fragility, and implementations, Rev Mod Phys, 90(2018)025004; doi.org/10.1103/RevModPhys.90.025004.
  11. Haake F, Kús M, Scharf R, Classical and quantum chaos for a kicked top, Zeitschrift für Physik B, Condensed Matter, 65(1987)381–395.
  12. Haake F, Quantum Signatures of Chaos, (Spring-Verlag, Berlin), 1991.
  13. Peres A, Quantum Theory: Concepts and Methods, (Kluwer Academic Publishers, New York), 2002.
  14. Ghose S, Sanders B C, Entanglement dynamics in chaotic systems, Phys Rev A, 70(2004)062315; doi.org/10.1103/PhysRevA.70.062315.
  15. Chaudhury S, Smith A, Anderson B E, Ghose S, Jessen P S, Quantum signatures of chaos in a kicked top, Nature, 461(2009)768–771.
  16. Neill C, Roushan P, Fang M, Chen Y, Kolodrubetz M, Chen Z, Megrant A, Barends R, Campbell B, Chiaro B, Dunsworth A, Jeffrey E, Kelly J, Mutus J, O’Malley P J J, Quintana C, Sank D, Vainsencher A, Wenner J, White C, Polkovnikov A, Martinis J M, Ergodic dynamics and thermalization in an isolated quantum system, Nat Phys, 12(2016)1037–1041.
  17. Dogra S, Madhok V, Lakshminarayan A Quantum signatures of chaos, thermalization, and tunneling in the exactly solvable few-body kicked top, Phys Rev E, 99(2019)062217; doi.org/10.1103/PhysRevE.99.062217.
  18. Kalaga J K, Kowalewska-Kudlaszyk A, Nowotarski M, Leoński W, Violation of leggett–garg inequalities in a kerr-type chaotic system, Photonics, 8(2021); doi.10.3390/photonics8010020.
  19. v d Vaart A W, Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, (Cambridge University Press), 1998.
  20. Ruebeck J B, Lin J, Pattanayak A K, Entanglement and its relationship to classical dynamics, Phys Rev E, 95(2017)062222; doi.org/10.1103/PhysRevE.95.062222.
  21. Dakna M, Clausen J, Knoll L, Welsch D G, Generating and monitoring Schrodinger cats in conditional measurement on beam splitter, Acta Phys Slov, 48(1998)207–220.
  22. Hamazaki R, Fujimoto K, Ueda M, Operator noncommutativity and irreversibility in quantum chaos, (2018), arXiv:1807.02360 [cond-mat.stat-mech].
  23. Jalabert R A, García-Mata, Wisniacki D A, Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems, Phys Rev E, 98 (2018)062218; doi.org/10.1103/PhysRevE.98.062218.
  24. Xu S, Swingle B, Scrambling dynamics and out-of-time-ordered correlators in quantum many-body systems, PRX Quantum, 5(2024)010201; doi.org/10.1103/PRXQuantum.5.010201.
  25. Dakna M, Clausen J, Knöll L, Welsch D G, Generation of arbitrary quantum states of traveling fields, Phys Rev A, 59(1999)1658; doi.org/10.1103/PhysRevA.59.1658.
  26. For a uniform random variable tβ, such a time average correctly gives the ensemble average for dn. Same holds for higher moments.
  27. Glauber R J, Haake F, Superradiant pulses and directed angular momentum states, Phys Rev A, 13(1976)357; doi.org/10.1103/PhysRevA.13.357 .
  28. Radcliffe J M, Some properties of coherent spin states, J Phys. A Math Gen, 4(1971)313; doi.10.1088/0305-4470/4/3/009.
  29. Ghose S, Stock R, Jessen P, Lal R, Silberfarb A, Chaos, entanglement, and decoherence in the quantum kicked top, Phys Rev A, 78(2008)042318; doi.org/10.1103/PhysRevA.78.042318.
  30. Berry M V, Evolution of semiclassical quantum states in phase space, J Phys. A Math Gen, 12(1979)625; doi. 10.1088/0305-4470/12/5/012.
  31. Chirikov B, F. Izrailev, Shepelyansky D, Quantum chaos: localization vs. ergodicity, Physica D: Nonlinear Phenomena, 33(1988)77–88.
  32. Karkuszewski Z P, Zakrzewski J, Zurek W H, Breakdown of correspondence in chaotic systems: Ehrenfest versus localization times, Phys Rev A, 65(2002)042113; doi.org/10.1103/PhysRevA.65.042113.
  33. Sakurai J J, Napolitano J, Modern Quantum Mechanics, 2nd edn, (Cambridge University Press), 2017.

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