  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.
