  The quantum reference frames program is based on the idea that reference
frames should be treated as quantum physical systems. In this work, we combine
these insights with the emphasis on operationality, understood as refraining
from introducing into the framework objects not directly related to in
principle verifiable probabilities of measurement outcomes, and identifying the
setups indistinguishable as such. Based on intuitions from special relativity
and gauge theory, we introduce an operational notion of a quantum reference
frame -- which is defined as a quantum system equipped with a covariant
positive operator-valued measure (POVM) -- and build a framework on the concept
of operational equivalence that allows us to enforce operationality by
quotienting the quantum state spaces with equivalence relation of
indistinguishability by the available effects, assumed to be invariant under
gauge transformations, and framed in the sense of respecting the choice of the
frame's POVM. Such effects are accessed via the yen construction, which maps
effects on the system to those on the composite system, satisfying gauge
invariance and framing. They are called relative, and the classes of states
indistinguishable by them are referred to as relative states. We show that when
the frame is localizable, meaning that it allows for states that give rise to a
highly localized probability distribution of the frame's observable, by
restricting the relative description upon such localized frame preparation we
recover the usual, non-relational formalism of quantum mechanics. We provide a
consistent way of translating between different relative descriptions by means
of frame-change maps and compare these with the corresponding notions in other
approaches to QRF, establishing an operational agreement in the domain of
common applicability.
