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

TL;DR

This paper reveals a conservation law linking entanglement and subsystem coherence under quantum reference frame transformations, deepening understanding of quantum resources and their invariance properties.

Contribution

It establishes a trade-off and conservation theorem for entanglement and coherence measures under QRF transformations, advancing quantum resource theory.

Findings

Sum of entanglement and coherence is invariant under QRF transformations.

Weaker trade-off exists for any pair of measures.

Implications for Bell inequality violations are clarified.

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.