Quantum scrambling of observable algebras

Paolo Zanardi

Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra $\cal A$ of operators evolving through a unitary channel. Qualitatively, quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. Quantitatively, this is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC), of the self-orthogonalization of the commutant of $\cal A$ induced by the dynamics. This approach extends and unifies averaged bipartite OTOC, operator entanglement, coherence generating power and Loschmidt echo. Each of these concepts is indeed recovered by a special choice of $\cal A$. We compute typical values of GAAC for random unitaries, we prove upper bounds and characterize their saturation. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between $\cal A$ and the full system of Hamiltonian eigenstates. Finally, a notion of ${\cal A}$-chaoticity is suggested.

► BibTeX data

► References

[1] A. Larkin and Y. N. Ovchinnikov, Sov Phys JETP 28, 1200 (1969).

[2] A. Kitaev, ``A simple model of quantum holography,'' http:/​/​online.kitp.ucsb.edu/​online/​entangled15/​kitaev/​ (2015).
http:/​/​online.kitp.ucsb.edu/​online/​entangled15/​kitaev/​

[3] J. Maldacena, S. H. Shenker, and D. Stanford, Journal of High Energy Physics 2016, 106 (2016), arXiv:1503.01409 [hep-th].
https:/​/​doi.org/​10.1007/​JHEP08(2016)106
arXiv:1503.01409

[4] D. A. Roberts and D. Stanford, Phys. Rev. Lett. 115, 131603 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.131603

[5] J. Polchinski and V. Rosenhaus, Journal of High Energy Physics 2016, 1 (2016), arXiv:1601.06768 [hep-th].
https:/​/​doi.org/​10.1007/​JHEP04(2016)001
arXiv:1601.06768

[6] M. Mezei and D. Stanford, Journal of High Energy Physics 2017, 65 (2017), arXiv:1608.05101 [hep-th].
https:/​/​doi.org/​10.1007/​JHEP05(2017)065
arXiv:1608.05101

[7] D. A. Roberts and B. Yoshida, Journal of High Energy Physics 2017, 121 (2017).
https:/​/​doi.org/​10.1007/​JHEP04(2017)121

[8] P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001a).
https:/​/​doi.org/​10.1103/​PhysRevLett.87.077901

[9] P. Zanardi, D. A. Lidar, and S. Lloyd, Phys. Rev. Lett. 92, 060402 (2004).
https:/​/​doi.org/​10.1103/​PhysRevLett.92.060402

[10] O. Kabernik, Phys. Rev. A 97, 052130 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.97.052130

[11] O. Kabernik, J. Pollack, and A. Singh, Phys. Rev. A 101, 032303 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.101.032303

[12] S. M. Carroll and A. Singh, Phys. Rev. A 103, 022213 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.022213

[13] P. Zanardi, Physical Review A 63, 040304 (2001b).
https:/​/​doi.org/​10.1103/​PhysRevA.63.040304

[14] T. c. v. Prosen and I. Pižorn, Phys. Rev. A 76, 032316 (2007).
https:/​/​doi.org/​10.1103/​PhysRevA.76.032316

[15] B. Yan, L. Cincio, and W. H. Zurek, Physical Review Letters 124, 160603 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.160603

[16] G. Styliaris, N. Anand, and P. Zanardi, Phys. Rev. Lett. 126, 030601 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.030601

[17] P. Zanardi, G. Styliaris, and L. Campos Venuti, Physical Review A 95 (2017a), 10.1103/​PhysRevA.95.052306.
https:/​/​doi.org/​10.1103/​PhysRevA.95.052306

[18] P. Zanardi, G. Styliaris, and L. Campos Venuti, Physical Review A 95 (2017b), 10.1103/​PhysRevA.95.052307.
https:/​/​doi.org/​10.1103/​PhysRevA.95.052307

[19] G. Styliaris, L. Campos Venuti, and P. Zanardi, Physical Review A 97 (2018), 10.1103/​PhysRevA.97.032304.
https:/​/​doi.org/​10.1103/​PhysRevA.97.032304

[20] R. A. Jalabert and H. M. Pastawski, Physical Review Letters 86, 2490 (2001a).
https:/​/​doi.org/​10.1103/​PhysRevLett.86.2490

[21] A. Goussev, R. A. Jalabert, H. M. Pastawski, and D. A. Wisniacki, Scholarpedia 7, 11687 (2012a).
https:/​/​doi.org/​10.4249/​scholarpedia.11687

[22] P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997).
https:/​/​doi.org/​10.1103/​PhysRevLett.79.3306

[23] D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.81.2594

[24] E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
https:/​/​doi.org/​10.1103/​PhysRevLett.84.2525

[25] P. Zanardi, Phys. Rev. A 63, 012301 (2000).
https:/​/​doi.org/​10.1103/​PhysRevA.63.012301

[26] A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys. 89, 041003 (2017).
https:/​/​doi.org/​10.1103/​RevModPhys.89.041003

[27] P. Zanardi and L. Campos Venuti, Journal of Mathematical Physics 59, 012203 (2018).
https:/​/​doi.org/​10.1063/​1.4997146

[28] P. Zanardi, G. Styliaris, and L. Campos Venuti, Phys. Rev. A 95, 052307 (2017c).
https:/​/​doi.org/​10.1103/​PhysRevA.95.052307

[29] A. Peres, Physical Review A 30, 1610 (1984).
https:/​/​doi.org/​10.1103/​PhysRevA.30.1610

[30] R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001b).
https:/​/​doi.org/​10.1103/​PhysRevLett.86.2490

[31] A. Goussev, R. A. Jalabert, H. M. Pastawski, and D. A. Wisniacki, Scholarpedia 7, 11687 (2012b), revision #127578.
https:/​/​doi.org/​10.4249/​scholarpedia.11687

[32] T. Gorin, T. Prosen, T. H. Seligman, and M. Žnidarič, Physics Reports 435, 33 (2006).
https:/​/​doi.org/​10.1016/​j.physrep.2006.09.003

[33] X. Wang and P. Zanardi, Phys. Rev. A 66, 044303 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.66.044303

[34] X. Chen and T. Zhou, arXiv:1804.08655 (2018).
arXiv:1804.08655

[35] V. Alba, J. Dubail, and M. Medenjak, Phys. Rev. Lett. 122, 250603 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.250603

[36] B. Bertini, P. Kos, and T. Prosen, SciPost Phys. 8, 67 (2020a).
https:/​/​doi.org/​10.21468/​SciPostPhys.8.4.067

[37] B. Bertini, P. Kos, and T. Prosen, SciPost Phys. 8, 68 (2020b).
https:/​/​doi.org/​10.21468/​SciPostPhys.8.4.068

[38] X. Mi et al., Science (2021).
https:/​/​doi.org/​10.1126/​science.abg5029

[39] G. Styliaris, N. Anand, L. C. Venuti, and P. Zanardi, Physical Review B 100, 224204 (2019), arXiv:1906.09242.
https:/​/​doi.org/​10.1103/​PhysRevB.100.224204
arXiv:1906.09242

[40] N. Anand, G. Styliaris, M. Kumari, and P. Zanardi, Phys. Rev. Research 3, 023214 (2021).
https:/​/​doi.org/​10.1103/​PhysRevResearch.3.023214

[41] L. C. Venuti and P. Zanardi, Physical Review A 81, 022113 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.81.022113

[42] P. Reimann, Physical Review Letters 101 (2008), 10.1103/​PhysRevLett.101.190403.
https:/​/​doi.org/​10.1103/​PhysRevLett.101.190403

Cited by

On Crossref's cited-by service no data on citing works was found (last attempt 2022-05-28 20:07:05). On SAO/NASA ADS no data on citing works was found (last attempt 2022-05-28 20:07:06).