A Remark on Quantum Measuring Systems and the Holographic Principle

Document Type : Regular article

Author

Graduate School of Human and Environmental Studies, Kyoto University

Abstract

It is a sort of ultimate question to examine the continuity of a quantum measurement subject theoretically and has not yet been resolved within a scientific framework.

In this article, we approach this question and argue that the continuity of a quantum measurement subject follows as a fundamental consequence of the holographic principle after the classicalization of the quantum state of the bulk space.

Keywords

Main Subjects

 [1] G. ’t Hooft, arXiv:gr-qc/9310026. DOI: 10.48550/arXiv.gr-qc/9310026
[2] L. Susskind, “The world as a hologram”, J. Math. Phys. 36, 6377 (1995). DOI: 10.1063/1.531249
[3] R. Bousso, “The holographic principle”, Rev. Mod. Phys. 74, 825 (2002). DOI: 10.1103/RevModPhys.74.825
[4] J. M. Maldacena, “The large-N limit of superconformal field theories and supergravity”, Adv. Theor. Math. Phys. 2, 231 (1998). DOI: 10.1023/A:1026654312961
[5] O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large-N field theories, string theory and gravity”, Phys. Rep. 323, 183 (2000). DOI: 10.1016/S0370-1573(99)00083-6
[6] E. Konishi, “Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 129, 11006 (2020). DOI: 10.1209/0295-5075/129/11006
[7] E. Konishi, “Addendum: Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 132, 59901 (2020). DOI: 10.1209/0295-5075/132/59901
[8] E. Konishi, “Imaginary-time path-integral in bulk space from the holographic principle”, JHAP 1, (1) 47-56 (2021). DOI: 10.22128/jhap.2021.432.1001
[9] B. d’Espagnat, Conceptual Foundations of Quantum Mechanics. 2nd edn. W. A. Benjamin, Reading, Massachusetts (1976).
[10] E. Konishi, “Quantum measuring systems: considerations from the holographic principle”, JHAP 3, (1) 31-38 (2023). DOI: 10.22128/jhap.2023.652.1039
[11] G. Vidal, “Entanglement renormalization”, Phys. Rev. Lett. 99, 220405 (2007). DOI: 10.1103/PhysRevLett.99.220405
[12] G. Vidal, “Class of quantum many-body states that can be effciently simulated”, Phys. Rev. Lett. 101, 110501 (2008). DOI: 10.1103/PhysRevLett.101.110501
[13] B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012). DOI: 10.1103/PhysRevD.86.065007
[14] H. Araki, “A remark on Machida–Namiki theory of measurement”, Prog. Theor. Phys. 64, 719 (1980). DOI: 10.1143/PTP.64.719
[15] E. Konishi, “Projection hypothesis from the von Neumann-type interaction with a Bose–Einstein condensate”, EPL 136, 10004 (2021). DOI: 10.1209/0295-5075/ac335f
[16] J. von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton, NJ (1955).
[17] G. Tononi, M. Boly, M. Massimini and C. Koch, “Integrated information theory: from consciousness to its physical substrate”, Nat. Rev. Neurosci. 17, 450 (2016). DOI: 10.1038/nrn.2016.44
[18] D. Balduzzi and G. Tononi, “Integrated information in discrete dynamical systems: motivation and theoretical framework”, PLoS. Comput. Biol. 4, e1000091 (2008). DOI: 10.1371/journal.pcbi.1000091
[19] D. Balduzzi and G. Tononi, “Qualia: the geometry of integrated information”, PLoS. Comput. Biol. 5, e1000462 (2009). DOI: 10.1371/journal.pcbi.1000462
[20] M. Oizumi, L. Albantakis and G. Tononi, “From the phenomenology to the mechanisms of consciousness: integrated information theory 3.0”, PLoS. Comput. Biol. 10, e1003588 (2014). DOI: 10.1371/journal.pcbi.1003588
[21] L. Albantakis, L. Barbosa, G. Findlay, M. Grasso, A. M. Haun, W. Marshall, et al., “Integrated information theory (IIT) 4.0: formulating the properties of phenomenal existence in physical terms”, PLoS. Comput. Biol. 19, e1011465 (2023). DOI: 10.1371/journal.pcbi.1011465 
Volume 3, Issue 4
November 2023
Pages 81-87
  • Receive Date: 27 October 2023
  • Revise Date: 27 November 2023
  • Accept Date: 27 November 2023