Quantum processes can be divided into two categories: unitary and non-unitary
ones. For a given quantum process, we can define a \textit{degree of the
unitarity (DU)} of this process to be the fidelity between it and its closest
unitary one. The DU, as an intrinsic property of a given quantum process, is
able to quantify the distance between the process and the group of unitary
ones, and is closely related to the noise of this quantum process. We derive
analytical results of DU for qubit unital channels, and obtain the lower and
upper bounds in general. The lower bound is tight for most of quantum
processes, and is particularly tight when the corresponding DU is sufficiently
large. The upper bound is found to be an indicator for the tightness of the
lower bound. Moreover, we study the distribution of DU in random quantum
processes with different environments. In particular, The relationship between
the DU of any quantum process and the non-markovian behavior of it is also
addressed.Comment: 7 pages, 2 figure
