The process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature
Communications {\bf3}, 1092 (2012)] can describe general physical theory where
locally operations are described by completely-positive maps but globally no
fixed causal structure is assumed. In this framework, two parties who perform
measurements on each single-qubit system can violate a "causal inequality",
which is not violated if the global fixed causal structure exists. Since the
standard quantum physics assumes a fixed global causal structure, the process
matrix framework can describe more general physical theory than the standard
quantum physics. In this paper, we show that for a single-party system the
process matrix framework is reduced to the standard quantum physics, and
therefore no exotic effect beyond the standard quantum physics can be observed.
This result is analogous to the well known fact in the Bell inequality
violation: a single-party system can be described by a local hidden variable
theory, whereas more than two parties can violate the Bell inequality.