  A Markovian quantum process can be arbitrarily divided into two or more
legitimate completely-positive (CP) subprocesses. When at least one non-CP
process exists among the divided processes, the dynamics is considered
non-Markovian. However, how to utilize minimum experimental efforts, without
examining all process input states and using entanglement resources, to
identify or measure non-Markovianity is still being determined. Herein, we
propose a method to quantify non-CP processes for identifying and measuring
non-Markovianity without the burden of state optimization and entanglement.
This relies on the non-CP processes as new quantum process capabilities and can
be systematically implemented by quantum process tomography. We additionally
provide an approach for witnessing non-Markovianity by analyzing at least four
system states without process tomography. We faithfully demonstrate that our
method can be explicitly implemented using all-optical setups and applied to
identify the non-Markovianity of single-photon and two-photon dynamics in
birefringent crystals. Our results can also be used to explore non-Markovianity
in other dynamical systems where process or state tomography is implementable.
