  Master equations govern the time evolution of a quantum system interacting
with an environment, and may be written in a variety of forms. Time-independent
or memoryless master equations, in particular, can be cast in the well-known
Lindblad form. Any time-local master equation, Markovian or non-Markovian, may
in fact also be written in a Lindblad-like form. A diagonalisation procedure
results in a unique, and in this sense canonical, representation of the
equation, which may be used to fully characterize the non-Markovianity of the
time evolution. Recently, several different measures of non-Markovianity have
been presented which reflect, to varying degrees, the appearance of negative
decoherence rates in the Lindblad-like form of the master equation. We
therefore propose using the negative decoherence rates themselves, as they
appear in the canonical form of the master equation, to completely characterize
non-Markovianity. The advantages of this are especially apparent when more than
one decoherence channel is present. We show that a measure proposed by Rivas et
al. is a surprisingly simple function of the canonical decoherence rates, and
give an example of a master equation that is non-Markovian for all times t>0,
but to which nearly all proposed measures are blind. We also give necessary and
sufficient conditions for trace distance and volume measures to witness
non-Markovianity, in terms of the Bloch damping matrix.
