  Several ways have been proposed in the literature to define a coherence
measure based on Tsallis relative entropy. One of them is defined as a distance
between a state and a set of incoherent states with Tsallis relative entropy
taken as a distance measure. Unfortunately, this measure does not satisfy the
required strong monotonicity, but a modification of this coherence has been
proposed that does. We introduce three new Tsallis coherence measures coming
from a more general definition that also satisfy the strong monotonicity, and
compare all five definitions between each other. Using three coherence measures
that we discuss, one can also define a discord. Two of these have been used in
the literature, and another one is new. We also discuss two correlation
measures based on Tsallis relative entropy. We provide explicit expressions for
all three discord and two correlation measure on pure states. Lastly, we
provide tight upper and lower bounds on two discord and correlations measures
on any quantum state, with the condition for equality.
