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Tsallis entropy is a useful one-parameter generalization of the standard vonNeumann entropy in information theory. We study the variance of Tsallis entropyof bipartite quantum systems in a random pure state. The main result is anexact variance formula of Tsallis entropy that involves finite sums of someterminating hypergeometric functions. In the special cases of quadratic entropyand small subsystem dimensions, the main result is further simplified toexplicit variance expressions. As a byproduct, we find an independent proof ofthe recently proved variance formula of von Neumann entropy based on thederived moment relation to the Tsallis entropy.

On the exact variance of Tsallis entropy in a random pure state