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Recently, some attention has been given to the so-called Page-Woottersmechanism of quantum clocks. Among the various proposals to explore themechanism using more modern techniques, some have chosen to use a quantuminformation perspective, defining and using informational measures to quantifyhow well a quantum system can stand as a reference frame for other quantumsystem. In this work, we explore the proposal based on resource theory ofasymmetry, known as mutual or shared asymmetry, which actually is equivalent tothe approach from coherence theory in the case of interest here: quantumreference frames described by the $U(1)$ compact group. We extend some previousresults in literature about shared asymmetry and Page-Wootters mechanism tomore general cases, culminating in the enunciation of a theorem relating sharedasymmetry of a bipartite state $\rho_{SR}$ with the relative entropy ofentanglement of \textit{internal states} $\rho_M$ on the charge sectors of theHilbert space $\mathcal{H}_S\otimes\mathcal{H}_R$. Using this result wereinterpret the relation between Page-Wootters mechanism and entanglement andalso open some paths to further studies.

Quantifying resources for Page-Wootters mechanism: Shared asymmetry as relative entropy of entanglement