  Quantum measurement and quantum operation theory is developed here by taking
the relational properties among quantum systems, instead of the independent
properties of a quantum system, as the most fundamental elements. By studying
how the relational probability amplitude matrix is transformed and how mutual
information is exchanged during measurement, we derive the formulation that is
mathematically equivalent to the traditional quantum measurement theory. More
importantly, the formulation results in significant conceptual consequences. We
show that for a given quantum system, it is possible to describe its time
evolution without explicitly calling out a reference system. However,
description of a quantum measurement must be explicitly relative. Traditional
quantum mechanics assumes a super observer who can instantaneously know the
measurement results from any location. For a composite system consists
space-like separated subsystems, the assumption of super observer must be
abandoned and the relational formulation of quantum measurement becomes
necessary. This is confirmed in the resolution of EPR paradox. Information
exchange is relative to a local observer in quantum mechanics. Different local
observers can achieve consistent descriptions of a quantum system if they are
synchronized on the information regarding outcomes from any measurement
performed on the system. It is suggested that the synchronization of
measurement results from different observers is a necessary step when combining
quantum mechanics with the relativity theory.
