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The Page-Wootters mechanism questioned the fundamental nature of time inquantum physics. The mechanism explored the notion that a given physicalquantity is always defined and measured relative to a reference frame, ingeneral, not explained in the theoretical description of quantum physicalexperiments. Recently, the resource theory of asymmetry deals explicitly withwhat are the physical conditions for a quantum system to serve as a goodreference frame. Nonetheless, to quantify a quantum reference frame in relationto another one it is a important task to establish an internal description ofquantum theory, i.e., without the need of a classical reference frame. In thiswork we address this issue by the concept of mutual asymmetry and use thismachinery in the Page-Wootters mechanism by identifying the concept of mutualasymmetry as mutual or internal coherence. To do so, the notion of quantumcoherence in relation of a quantum reference frame is revisited and aquantifier is proposed in this scenario. Also, this open space to investigatethe link of internal coherence and correlations, as proposed by Page andWootters, under a resource theory approach.

Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries