Measurement of a quantum particle position at two distant locations: a model

Authors

  • Jaroslav Dittrich Czech Academy of Sciences, Nuclear Physics Institute, 250 68 Řež, Czech Republic

DOI:

https://doi.org/10.14311/AP.2022.62.0445

Keywords:

position measurement, EPR paradox, quantum measurement

Abstract

A simplified one-dimensional model of measurement of the position of a quantum particle by two distant detectors is considered. Detectors are modelled by quantum particles bounded in potential wells with just two bound states, prepared in the excited states. Their de-excitation due to the short range interaction with the measured particle is the signal for the detection. In the approximations of short time or small coupling between the particle and the measuring apparatuses, the simultaneous detection of the particle by both detectors is suppressed. The results extend to other models with two-level detectors.

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References

J. von Neumann. Mathematical Foundations of Quantum Mechanics. Princeton University Press, 2018.

A. A. Clerk, M. H. Devoret, S. M. Girvin, et al. Introduction to quantum noise, measurement, and amplification. Reviews of Modern Physics 82(2):1155–1208, 2010. https://doi.org/10.1103/RevModPhys.82.1155.

A. E. Allahverdyan, R. Balian, T. M. Nieuwenhuizen. Understanding quantum measurement from the solution of dynamical models. Physics Reports 525(1):1–166, 2013. https://doi.org/10.1016/j.physrep.2012.11.001.

J. Zhang, Y. xi Liu, R.-B. Wu, et al. Quantum feedback: Theory, experiments, and applications. Physics Reports 679:1–60, 2017. https://doi.org/10.1016/j.physrep.2017.02.003.

B. d’Espagnat. Conceptual Foundations of Quantum Mechanics. CRC Press, Boca Raton, 2nd edn., 2019.

C. Beck. Local Quantum Measurement and Relativity. Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-67533-2.

F. Pokorny, C. Zhang, G. Higgins, et al. Tracking the dynamics of an ideal quantum measurement. Physical Review Letters 124(8-28):080401, 2020. https://doi.org/10.1103/PhysRevLett.124.080401.

J. Polo-Gómez, L. J. Garay, E. Martín-Martínez. A detector-based measurement theory for quantum field theory. Physical Review D 105:065003, 2022. https://doi.org/10.1103/PhysRevD.105.065003.

A. Einstein, B. Podolsky, N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Physical Review 47:777–780, 1935. https://doi.org/10.1103/PhysRev.47.777.

I. Bengtsson, K. Życzkowski. Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, 2017. https://doi.org/10.1017/9781139207010.

K. Zyczkowski, I. Bengtsson. An introduction to quantum entanglement: A geometric approach, 2006. https://doi.org/10.48550/ARXIV.QUANT-PH/0606228.

N. Friis, G. Vitagliano, M. Malik, M. Huber. Entanglement certification from theory to experiment. Nature Reviews Physics 1:72–87, 2019. https://doi.org/10.1038/s42254-018-0003-5.

P. Meystre. Quantum Optics: Taming the Quantum. Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-76183-7.

D. D’Alessandro. Introduction to Quantum Control and Dynamics. CRC Press, Boca Raton, 2021. https://doi.org/10.1201/9781003051268.

M. Fadel. Many-particle entanglement, Einstein-Podolsky-Rosen steering and Bell correlations in Bose-Einstein condensates. Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-85472-0.

M. Kupczynski. Seventy years of the EPR paradox. AIP Conference Proceedings 861:516–523, 2006. https://doi.org/10.1063/1.2399618.

L. Susskind. ER=EPR, GHZ, and the consistency of quantum measurements. Fortschritte der Physik 64:72–83, 2016. https://doi.org/10.1002/prop.201500094.

W. Zhang, M.-X. Dong, D.-S. Ding, et al. Einstein-Podolsky-Rosen entanglement between separated atomic ensembles. Physical Review A 100(1):012347, 2019. https://doi.org/10.1103/PhysRevA.100.012347.

M. Fadel, A. Usui, M. Huber, et al. Entanglement quantification in atomic ensembles. Physical Review Letters 127(1):010401, 2021. https://doi.org/10.1103/PhysRevLett.127.010401.

P. Marian, T. A. Marian. Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states. Physical Review A 103(6):062224, 2021. https://doi.org/10.1103/PhysRevA.103.062224.

W. Zhong, D. Zhao, G. Cheng, A. Chen. One-way Einstein–Podolsky–Rosen steering of macroscopic magnons with squeezed light. Optics Communications 497:127138, 2021. https://doi.org/10.1016/j.optcom.2021.127138.

K. Berrada, H. Eleuch. Einstein-Podolsky-Rosen steering and nonlocality in quantum dot systems. Physica E: Lowdimensional Systems and Nanostructures 126:114412, 2021. https://doi.org/10.1016/j.physe.2020.114412.

Y. Xiang, X. Su, L. Mišta, et al. Multipartite Einstein-Podolsky-Rosen steering sharing with separable states. Physical Review A 99(1):010104, 2019. https://doi.org/10.1103/PhysRevA.99.010104.

N. B. An. Quantum dialogue mediated by EPR-type entangled coherent states. Quantum Information Processing 20:100, 2021. https://doi.org/10.1007/s11128-021-03007-1.

O. V. Gritsenko. Quantum collapse as reduction from a continuum of conditional amplitudes in an entangled state to a single actualized amplitude in the collapsed state. Physical Review A 101(1):012106, 2020. https://doi.org/10.1103/PhysRevA.101.012106.

K. M. Frahm, D. L. Shepelyansky. Chaotic Einstein-Podolsky-Rosen pairs, measurements and time reversal. The European Physical Journal D 75:277, 2021. https://doi.org/10.1140/epjd/s10053-021-00274-6.

D. I. Blokhintsev. Fundamentals of Quantum Mechanics. Nauka, Moscow, 1976. In Russian.

S. Machida, M. Namiki. Theory of measurement in quantum mechanics I. Progress of Theoretical Physics 63(5):1457–1473, 1980. https://doi.org/10.1143/PTP.63.1457.

S. Machida, M. Namiki. Theory of measurement in quantum mechanics II. Progress of Theoretical Physics 63(6):1833–1847, 1980. https://doi.org/10.1143/PTP.63.1833.

D. Bohm. Quantum Theory. Prentice-Hall, New York, 1952.

K. Hepp. Quantum theory of mesurement and macroscopic observables. Helvetica Physica Acta 45:237–248, 1972. https://doi.org/10.5169/seals-114381.

M. Cini, M. De Maria, G. Mattioli, F. Nicolò. Wave packet reduction in quantum mechanics: A model of a measuring apparatus. Foundations of Physics 9:479–500, 1979. https://doi.org/10.1007/BF00708363.

P. Bóna. Classical Systems in Quantum Mechanics. Springer, Cham, 2020. https://doi.org/10.1007/978-3-030-45070-0.

M. Reed, B. Simon. Methods of Modern Mathematical Physics. II. Fourier Analysis. Self-Adjointness. Academic Press, San Diego, 1975.

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Published

2022-08-31

How to Cite

Dittrich, J. (2022). Measurement of a quantum particle position at two distant locations: a model. Acta Polytechnica, 62(4), 445–450. https://doi.org/10.14311/AP.2022.62.0445

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