Abstract
In contrast to the previous chapters, we deal in this chapter with quantum systems, and specifically, with the facet of noise in the sense of uncertainty associated with quantum measurements. This sort of noise is invariably of quantum origin, and we explore its manifestation in the set-up of a quantum system undergoing unitary evolution in time that is being repeatedly interrupted at random times with projective measurements collapsing the instantaneous state to the initial state of the system. Specifically, we ask: How does the survival probability, namely, the probability that an initial state survives even after a certain number m of measurements, behave as a function of m? We pursue our studies in the context of two paradigmatic quantum systems, one, the quantum random walk evolving in discrete times, and the other, the tight-binding model evolving in continuous time, with both defined on a one- dimensional periodic lattice constituted by a finite number of sites. We unveil a host of interesting results on the survival probability that point to the curious nature of quantum measurement dynamics. This chapter is based on our published work, Ref. [1].
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Notes
- 1.
In this chapter, we will take the Planck’s constant to be unity.
- 2.
- 3.
We will use the notation \(p(\tau )\) (respectively, \(p_\tau \)) to denote the distribution for the case when \(\tau \) is a continuous (respectively, a discrete) random variable.
References
D. Das, S. Gupta, J. Stat. Mech. 2022(3), 033212 (2022). https://doi.org/10.1088/1742-5468/ac5dc0
C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics, Volume 1: Basic Concepts, Tools, and Applications, 2nd edn. (Wiley-VCH, Weinheim, 2020)
B. Misra, E.C.G. Sudarshan, J. Math. Phys. 18(4), 756 (1977). https://doi.org/10.1063/1.523304
S. Gherardini, S. Gupta, F.S. Cataliotti, A. Smerzi, F. Caruso, S. Ruffo, New J. Phys. 18(1), 013048 (2016). https://doi.org/10.1088/1367-2630/18/1/013048
Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48(2), 1687 (1993). https://doi.org/10.1103/PhysRevA.48.1687
D.H. Dunlap, V.M. Kenkre, Phys. Rev. B 34(6), 3625 (1986). https://doi.org/10.1103/PhysRevB.34.3625
D. Dunlap, V. Kenkre, Phys. Lett. A 127(8–9), 438 (1988). https://doi.org/10.1016/0375-9601(88)90213-7
M.M. Müller, S. Gherardini, F. Caruso, Annalen der Physik 529(9), 1600206 (2017). https://doi.org/10.1002/andp.201600206
S. Gherardini, C. Lovecchio, M.M. Müller, P. Lombardi, F. Caruso, F.S. Cataliotti, Quantum. Sci. Technol. 2(1), 015007 (2017). https://doi.org/10.1088/2058-9565/aa5d00
S. Gherardini, L. Buffoni, M.M. Müller, F. Caruso, M. Campisi, A. Trombettoni, S. Ruffo, Phys. Rev. E 98(3), 032108 (2018). https://doi.org/10.1103/PhysRevE.98.032108
H.V. Do, C. Lovecchio, I. Mastroserio, N. Fabbri, F.S. Cataliotti, S. Gherardini, M.M. Müller, N. Dalla Pozza, F. Caruso, New J. Phys. 21(11), 113056 (2019). https://doi.org/10.1088/1367-2630/ab5740
R.S. Ellis, Entropy, Large Deviations, and Statistical Mechanics (Springer. Berlin, 2006). https://doi.org/10.1007/3-540-29060-5
H. Touchette, Phys. Rep. 478(1–3), 1 (2009). https://doi.org/10.1016/j.physrep.2009.05.002
S. Dhar, S. Dasgupta, A. Dhar, J. Phys. A: Math. Theor. 48(11), 115304 (2015). https://doi.org/10.1088/1751-8113/48/11/115304
S. Dhar, S. Dasgupta, A. Dhar, D. Sen, Phys. Rev. A 91(6), 062115 (2015). https://doi.org/10.1103/PhysRevA.91.062115
H. Friedman, D.A. Kessler, E. Barkai, J. Phys. A: Math. Theor. 50(4), 04LT01 (2017). https://doi.org/10.1088/1751-8121/aa5191
H. Friedman, D.A. Kessler, E. Barkai, Phys. Rev. E 95(3), 032141 (2017). https://doi.org/10.1103/PhysRevE.95.032141
F. Thiel, E. Barkai, D.A. Kessler, Phys. Rev. Lett. 120(4), 040502 (2018). https://doi.org/10.1103/PhysRevLett.120.040502
F. Thiel, I. Mualem, D.A. Kessler, E. Barkai, Quantum total detection probability from repeated measurements II. Exploiting symmetry (2019). https://doi.org/10.48550/arXiv.1909.02114
S. Lahiri, A. Dhar, Phys. Rev. A 99(1), 012101 (2019). https://doi.org/10.1103/PhysRevA.99.012101
D. Meidan, E. Barkai, D.A. Kessler, J. Phys. A: Math. Theor. 52(35), 354001 (2019). https://doi.org/10.1088/1751-8121/ab3305
R. Yin, K. Ziegler, F. Thiel, E. Barkai, Phys. Rev. Res. 1(3), 033086 (2019). https://doi.org/10.1103/PhysRevResearch.1.033086
F. Thiel, I. Mualem, D. Meidan, E. Barkai, D.A. Kessler, Phys. Rev. Res. 2(4), 043107 (2020). https://doi.org/10.1103/PhysRevResearch.2.043107
F. Thiel, I. Mualem, D.A. Kessler, E. Barkai, Phys. Rev. Res. 2(2), 023392 (2020). https://doi.org/10.1103/PhysRevResearch.2.023392
V. Dubey, C. Bernardin, A. Dhar, Phys. Rev. A 103(3), 032221 (2021). https://doi.org/10.1103/PhysRevA.103.032221
F. Thiel, I. Mualem, D. Kessler, E. Barkai, Entropy 23(5), 595 (2021). https://doi.org/10.3390/e23050595
Q. Liu, K. Ziegler, D.A. Kessler, E. Barkai, Phys. Rev. Res. 4(2), 023129 (2022). https://doi.org/10.1103/PhysRevResearch.4.023129
D.A. Kessler, E. Barkai, K. Ziegler, Phys. Rev. A 103(2), 022222 (2021). https://doi.org/10.1103/PhysRevA.103.022222
A. Nayak, A. Vishwanath (2000). arXiv:quant-ph/0010117
J. Kempe, Contemp. Phys. 44(4), 307 (2003). https://doi.org/10.1080/00107151031000110776
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Das, D., Gupta, S. (2023). Quantum Systems Subject to Random Projective Measurements. In: Facets of Noise. Fundamental Theories of Physics, vol 214. Springer, Cham. https://doi.org/10.1007/978-3-031-45312-0_10
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