Operations of Quantum Measuring Systems and the Holographic Principle

Document Type : Regular article

Author

Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan

Abstract

Based on the author's previous argument of the constant existence of the subject of quantum measurement in the framework of the classicalized holographic tensor network, for two quantum measuring systems $M_1$ and $M_2$ in the bulk spacetime, we calculate the result of the processes $(((M_1)_{\rm I}-M_1)_{\rm II}+M_2)_{\rm III}$ as the subject of quantum measurement. This process is obtained from the process $(((M_1)_{\rm I}+M_2)_{\rm II}-M_1)_{\rm III}$ by swapping processes II and III. The latter process is within the Lorentzian regime of spacetime and results in the quantum measuring system $M_2$. Therefore, we conclude that the objective result is also $M_2$.

Keywords

Main Subjects

 

Article PDF

 [1] E. Konishi, “Quantum measuring systems: considerations from the holographic principle”, JHAP 3(1), 31 (2023). DOI: 10.22128/jhap.2023.652.1039
[2] E. Konishi, “A remark on quantum measuring systems and the holographic principle”, JHAP 3(4), 81 (2023). DOI: 10.22128/jhap.2023.752.1064
[3] E. Konishi, “More on quantum measuring systems and the holographic principle”, JHAP 4(3), 11 (2024). DOI: 10.22128/jhap.2024.866.1092
[4] G. ’t Hooft, DOI: 10.48550/arXiv.gr-qc/9310026 [arXiv:gr-qc/9310026]
[5] L. Susskind, “The world as a hologram”, J. Math. Phys. 36, 6377 (1995). DOI: 10.1063/1.531249
[6] R. Bousso, “The holographic principle”, Rev. Mod. Phys. 74, 825 (2002). DOI: 10.1103/RevModPhys.74.825
[7] 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
[8] 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
[9] B. Swingle, “Entanglement renormalization and holography”, Phys. Rev. D 86, 065007 (2012). DOI: 10.1103/PhysRevD.86.065007
[10] H. Matsueda, M. Ishibashi and Y. Hashizume, “Tensor network and a black hole”, Phys. Rev. D 87, 066002 (2013). DOI: 10.1103/PhysRevD.87.066002
[11] N. Bao, C. Cao, S. M. Carroll, A. Chatwin-Davies and N. Hunter-Jones, “Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence”, Phys. Rev. D 91, 125036 (2015). DOI: 10.1103/PhysRevD.91.125036
[12] E. Konishi, “Holographic interpretation of Shannon entropy of coherence of quantum pure states”, EPL 129, 11006 (2020). DOI: 10.1209/0295-5075/129/11006
[13] 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
[14] E. Konishi, “Imaginary-time path-integral in bulk space from the holographic principle”, JHAP 1(1), 47 (2021). DOI: 10.22128/jhap.2021.432.1001
[15] B. d’Espagnat, Conceptual Foundations of Quantum Mechanics. 2nd edn. W. A. Benjamin, Reading, Massachusetts (1976).
[16] S. Machida and M. Namiki, “Theory of measurement of quantum mechanics: mechanism of reduction of wave packet. I”, Prog. Theor. Phys. 63, 1457 (1980). DOI: 10.1143/PTP.63.1457
[17] S. Machida and M. Namiki, “Theory of measurement of quantum mechanics: mechanism of reduction of wave packet. II”, Prog. Theor. Phys. 63, 1833 (1980). DOI: 10.1143/PTP.63.1833
[18] E. Konishi, “Work required for selective quantum measurement”, J. Stat. Mech. 063403 (2018). DOI: 10.1088/1742-5468/aac13f
[19] J. M. Jauch, “Systems of observables in quantum mechanics”, Helv. Phys. Acta. 33, 711 (1960).
[20] H. Araki, “A remark on Machida–Namiki theory of measurement”, Prog. Theor. Phys. 64, 719 (1980). DOI: 10.1143/PTP.64.719
[21] E. Konishi, “Addendum: Work required for selective quantum measurement”, J. Stat. Mech. 019501 (2019). DOI: 10.1088/1742-5468/aaf31f
[22] 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
[23] H. Umezawa, Advanced Field Theory: Micro, Macro and Thermal Physics. American Institute of Physics, New York (1993).
[24] J. Von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton, NJ (1955).
[25] E. Konishi, “Projection hypothesis in the setting for the quantum Jarzyski equality”, Int. J. Quantum Information 2450033 (2024). DOI: 10.1142/S0219749924500333
Volume 4, Issue 4
December 2024
Pages 15-20
  • Receive Date: 30 October 2024
  • Revise Date: 16 November 2024
  • Accept Date: 16 November 2024