Quantum Reference Frames for Lorentz Symmetry

Luca Apadula; Esteban Castro-Ruiz; Časlav Brukner

doi:10.22331/q-2024-08-14-1440

Quantum Reference Frames for Lorentz Symmetry

Luca Apadula^1,2, Esteban Castro-Ruiz³, and Časlav Brukner^1,2

¹Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
²Institute for Quantum Optics and Quantum Information (IQOQI-Vienna), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
³Institute for Theoretical Physics, ETH Zurich, Switzerland

Published:	2024-08-14, volume 8, page 1440
Eprint:	arXiv:2212.14081v2
Doi:	https://doi.org/10.22331/q-2024-08-14-1440
Citation:	Quantum 8, 1440 (2024).

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Abstract

Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.

► BibTeX data

@article{Apadula2024quantumreference,
  doi = {10.22331/q-2024-08-14-1440},
  url = {https://doi.org/10.22331/q-2024-08-14-1440},
  title = {Quantum {R}eference {F}rames for {L}orentz {S}ymmetry},
  author = {Apadula, Luca and Castro-Ruiz, Esteban and Brukner, {\v{C}}aslav},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1440},
  month = aug,
  year = {2024}
}

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[1] Matthew J. Lake and Marek Miller, "Quantum reference frames, revisited", arXiv:2312.03811, (2023).

[2] Viktoria Kabel, Anne-Catherine de la Hamette, Luca Apadula, Carlo Cepollaro, Henrique Gomes, Jeremy Butterfield, and Časlav Brukner, "Identification is Pointless: Quantum Reference Frames, Localisation of Events, and the Quantum Hole Argument", arXiv:2402.10267, (2024).

[3] Viktoria Kabel, Časlav Brukner, and Wolfgang Wieland, "Quantum reference frames at the boundary of spacetime", Physical Review D 108 10, 106022 (2023).

[4] Shadi Ali Ahmad, Wissam Chemissany, Marc S. Klinger, and Robert G. Leigh, "Quantum Reference Frames from Top-Down Crossed Products", arXiv:2405.13884, (2024).

[5] Carlo Cepollaro, Ali Akil, Paweł Cieśliński, Anne-Catherine de la Hamette, and Časlav Brukner, "The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations", arXiv:2406.19448, (2024).

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