Bipartite separability of symmetric N-qubit noisy states using conditional quantum relative Tsallis entropy

In any bipartition of a quantum state, it is proved that the negative values of the conditional version of sandwiched Tsallis relative entropy necessarily imply 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-, WW̄ 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 are brought out through this and other one-parameter families of states.