  Quantum operations represented by completely positive maps encompass many of
the physical processes and have been very powerful in describing quantum
computation and information processing tasks. We introduce the notion of
relative phase change for a quantum system undergoing quantum operation. We
find that the relative phase shift of a system not only depends on the state of
the system, but also depends on the initial state of the ancilla with which it
might have interacted in the past. The relative phase change during a sequence
of quantum operations is shown to be non-additive in nature. This property can
attribute a `memory' to a quantum channel. Also the notion of relative phase
shift helps us to define what we call `in-phase quantum channels'. We will
present the relative phase shift for a qubit undergoing depolarizing channel
and complete randomization and discuss their implications.
