Operational Quantum Reference Frame Transformations

Titouan Carette; Jan Glowacki; Leon Loveridge

doi:10.22331/q-2025-03-27-1680

Operational Quantum Reference Frame Transformations

Titouan Carette^1,2, Jan Glowacki^1,3,4,5,6, and Leon Loveridge^1,7,8

¹Basic Research Community for Physics, Leipzig, Germany
²LIX, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
³Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland
⁴International Center for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland
⁵Department of Computer Science, University of Oxford, OX1 3QD Oxford, UK
⁶Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
⁷Department of Science and Industry Systems, University of South-Eastern Norway, 3616 Kongsberg, Norway
⁸Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan

Published:	2025-03-27, volume 9, page 1680
Editor:	Maximilian Lock
Eprint:	arXiv:2303.14002v4
Doi:	https://doi.org/10.22331/q-2025-03-27-1680
Citation:	Quantum 9, 1680 (2025).

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Abstract

Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition of observable quantities. Though around since the 1960s, and used in a wide range of applications, only recently has the means for transforming descriptions between different quantum reference frames been tackled in detail. In this work, we provide a general, operationally motivated framework for quantum reference frames and their transformations, holding for locally compact groups. The work is built around the notion of operational equivalence, in which quantum states that cannot be physically distinguished are identified. For example, we describe the collection of relative observables as a subspace of the algebra of invariants on the composite of system and frame, and from here the set of relative states is constructed through the identification of states which cannot be distinguished by relative observables. Through the notion of framed observables – the formation of joint observables of system and frame – of which the relative observables can be understood as examples, quantum reference frame transformations are then maps between equivalence classes of relative states which respect the framing. We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable. The transformations are invertible exactly when the final frame also has such a localizability property. The procedure we present is in operational agreement with other recent inequivalent constructions on the domain of common applicability, but extends them in a number of ways, and weakens claims of entanglement generation through frame changes.

► BibTeX data

@article{Carette2025operationalquantum,
  doi = {10.22331/q-2025-03-27-1680},
  url = {https://doi.org/10.22331/q-2025-03-27-1680},
  title = {Operational {Q}uantum {R}eference {F}rame {T}ransformations},
  author = {Carette, Titouan and Glowacki, Jan and Loveridge, Leon},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1680},
  month = mar,
  year = {2025}
}

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