  Physical observation is made relative to a reference frame which is
essentially a quantum system. Thus, a quantum system must be described relative
to a quantum reference frame (QRF). Further requirements on QRF include using
only relational observables and not assuming the existence of external
reference frame. To address these requirements, two approaches are proposed in
the literature. The first one is an operational approach (F. Giacomini, et al,
Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation
between QRFs. The second approach attempts to derive the quantum transformation
between QRFs from first principles (A. Vanrietvelde, et al, \textit{Quantum}
4:225, 2020). Such first principle approach describes physical systems as
symmetry induced constrained Hamiltonian systems. The Dirac quantization of
such systems before removing redundancy is interpreted as perspective-neutral
description. Then, a systematic redundancy reduction procedure is introduced to
derive description from perspective of a QRF. The first principle approach
recovers some of the results from the operational approach, but not yet include
an important part of a quantum theory - the measurement theory. This paper is
intended to bridge the gap. We show that the von Neumann quantum measurement
theory can be embedded into the perspective-neutral framework. This allows us
to successfully recover the results found in the operational approach, with the
advantage that the transformation operator can be derived from the first
principle. In addition, the formulation presented here reveals several
interesting conceptual insights. For instance, the projection operation in
measurement needs to be performed after redundancy reduction. These results
represent one step forward in understanding how quantum measurement should be
formulated when the reference frame is also a quantum system.

Quantum Physics