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The quantum relative Renyi entropy of two density matrices was recentlyextended when the two do not commute, from which a conditional entropy isidentified. This is here extended to the corresponding Tsallis relative entropyand to its conditional form. This new expression of Tsallis conditional entropyis shown to witness entanglement beyond the method based on global and localspectra of composite quantum states. When the reduced density matrix happens tobe a maximally mixed state, this conditional entropy coincides with theexpression in terms of Tsallis entropies derived earlier by Abe and Rajagopal(Physica A 289, 157 (2001)). Separability range in one parameter family of Wand GHZ states with 3 and 4 qubits is explored here and it is shown that theresults inferred from negative Tsallis conditional entropy matches with thatobtained through Peres partial transpose criteria for one-parameter family of Wstates, in one of its partitions. The criteria is shown to be non-spectralthrough its usefulness in identifying entanglement in isospectral densitymatrices.

From the sandwiched quantum relative Tsallis entropy to its conditional form: Separability criterion beyond local and global spectra