  In any bipartition of a quantum state, it is proved that the negative values
of the conditional version of sandwiched Tsallis relative entropy necessarily
implies quantum entanglement. For any N, the separability ranges in the $1:N-1$
partition of symmetric one parameter families of noisy $N$-qubit W, GHZ, states
are determined using the conditional quantum relative Tsallis entropy approach.
The 1:N-1 separability range matches exactly with the range obtained through
positive partial transpose criterion, for all N. The advantages of using
non-commuting version of $q$-conditional relative Tsallis entropy is brought
out through this and other one-parameter families of states.
