The process matrix framework for a single-party system

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.