The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations

• URL: http://arxiv.org/abs/2406.19448v1
• Date: Thu, 27 Jun 2024 18:00:02 GMT
• Title: The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Authors: Carlo Cepollaro, Ali Akil, Paweł Cieśliński, Anne-Catherine de la Hamette, Časlav Brukner,
• Abstract summary: Recent work on quantum reference frames (QRFs) has demonstrated that superposition and entanglement are properties that change under QRF transformations. We find a trade-off between entanglement and subsystem coherence under a QRF transformation, in the form of a conservation theorem for their sum. We discuss the implications of this interplay for violations of Bell's inequalities.
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• License: http://creativecommons.org/licenses/by/4.0/
• 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 find a trade-off between entanglement and subsystem coherence under a QRF transformation, in the form of a conservation theorem for their sum, for two pairs of measures. Moreover, we find a weaker trade-off 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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