🔧На сайте запланированы технические работы
25.12.2025 в промежутке с 18:00 до 21:00 по Московскому времени (GMT+3) на сайте будут проводиться плановые технические работы. Возможны перебои с доступом к сайту. Приносим извинения за временные неудобства. Благодарим за понимание!
🔧Site maintenance is scheduled.
Scheduled maintenance will be performed on the site from 6:00 PM to 9:00 PM Moscow time (GMT+3) on December 25, 2025. Site access may be interrupted. We apologize for the inconvenience. Thank you for your understanding!

 

Quantum mereology in finite quantum mechanics

Capa

Citar

Texto integral

Resumo

Any Hilbert space with composite dimension can be factored into a tensor product of smaller Hilbert spaces. This allows us to decompose a quantum system into subsystems. We propose a model based on finite quantum mechanics for a constructive study of such decompositions.

Sobre autores

Vladimir Kornyak

Joint Institute for Nuclear Research

Autor responsável pela correspondência
Email: vkornyak@gmail.com
ORCID ID: 0000-0002-5712-2960

Doctor of Sciences in Physics and Mathematics, Leading researcher, Laboratory of Information Technologies

6, Joliot-Curie St., Dubna, Moscow Region, 141980, Russian Federation

Bibliografia

  1. D. N. Page and W. K. Wootters, “Evolution without evolution: dynamics described by stationary observables,” Phys. Rev. D, vol. 27, pp. 2885- 2892, 12 Jun. 1983. doi: 10.1103/PhysRevD.27.2885.
  2. S. M. Carroll and A. Singh, “Quantum mereology: factorizing Hilbert space into subsystems with quasiclassical dynamics,” Physical Review A, vol. 103, no. 2, Feb. 2021. doi: 10.1103/physreva.103.022213.
  3. C. Cao, S. M. Carroll, and S. Michalakis, “Space from Hilbert space: recovering geometry from bulk entanglement,” Physical Review D, vol. 95, no. 2, Jan. 2017. doi: 10.1103/physrevd.95.024031.
  4. M. Woods, “The Page-Wootters mechanism 36 years on: a consistent formulation which accounts for interacting systems,” Quantum Views, vol. 3, p. 16, Jul. 2019. doi: 10.22331/qv-2019-07-21-16.
  5. P. Zanardi, “Virtual quantum subsystems,” Physical Review Letters, vol. 87, no. 7, Jul. 2001. doi: 10.1103/physrevlett.87.077901.
  6. P. Zanardi, D. A. Lidar, and S. Lloyd, “Quantum tensor product structures are observable induced,” Physical Review Letters, vol. 92, no. 6, Feb. 2004. doi: 10.1103/physrevlett.92.060402.
  7. A. M. Gleason, “Measures on the closed subspaces of a Hilbert space,” Journal of Mathematics and Mechanics, vol. 6, no. 6, pp. 885-893, 1957.
  8. V. V. Kornyak, “Quantum models based on finite groups,” Journal of Physics: Conference Series, vol. 965, p. 012023, Feb. 2018. doi: 10.1088/1742-6596/965/1/012023.
  9. V. V. Kornyak, “Modeling quantum behavior in the framework of permutation groups,” in EPJ Web of Conferences. EDP Sciences, 2018, vol. 173, p. 01007. doi: 10.1051/epjconf/201817301007.
  10. V. V. Kornyak, “Mathematical modeling of finite quantum systems,” Lect. Notes Comput. Sci., vol. 7125, pp. 79-93, 2012. arXiv: 1107.5675 [quant-ph].
  11. T. Banks, “Finite deformations of quantum mechanics,” 2020. arXiv: 2001.07662[hep-th].
  12. M. J. Collins, “On Jordan’s theorem for complex linear groups,” Journal of Group Theory, vol. 10, no. 4, pp. 411-423, 2007. doi: 10.1515/JGT. 2007.032.
  13. A. Rényi, “On measures of entropy and information,” English, in Proc. 4th Berkeley Symp. Math. Stat. Probab. 1, 1961, pp. 547-561.
  14. M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav., vol. 42, pp. 2323-2329, 2010. doi: 10.1142/S0218271810018529. arXiv: 1005.3035[hep-th].
  15. J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortschritte der Physik, vol. 61, no. 9, pp. 781-811, Aug. 2013. doi: 10.1002/prop.201300020.
  16. M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, 10th anniversary edition. USA: Cambridge University Press, 2016.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML