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Sum of Entanglement and Subsystem Coherence Is Invariant under Quantum Reference Frame Transformations

Carlo Cepollaro1,2,*, Ali Akil3,†, Paweł Cieśliński4, Anne-Catherine de la Hamette1,2, and Časlav Brukner1,2

  • 1Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
  • 2Institute of Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
  • 3Department of Computer Science, The University of Hong Kong, Hong Kong Island, Hong Kong S.A.R. China
  • 4Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland

  • *Contact author: carlo.cepollaro@oeaw.ac.at
  • †Contact author: aliakil@hku.hk
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Phys. Rev. Lett. 135, 010201 – Published 30 June, 2025

DOI: https://doi.org/10.1103/h6b3-y4vt

Abstract

Recent work on quantum reference frames (QRFs) has demonstrated that superposition and entanglement are properties that change under QRF transformations. Given their utility in quantum information processing, it is important to understand how a mere change of perspective can produce or reduce these resources. Here we prove the existence of a QRF invariant which can be decomposed such that it captures the trade-off between entanglement and subsystem coherence: we demonstrate the invariance of the sum of entanglement and subsystem coherence for two pairs of resource quantifiers. Moreover, we find a weaker trade-off that holds for any possible pair of measures. Finally, we discuss the implications of this interplay for violations of Bell’s inequalities, clarifying that for any choice of QRF, there is a quantum resource responsible for the violation. These findings contribute to a better understanding of the quantum information theoretic aspects of QRFs, offering a foundation for future exploration in both quantum theory and quantum gravity.

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Phys. Rev. Lett. 135, 010201– Published 30 June, 2025
  • Received 2 August 2024
  • Accepted 28 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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