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

Abstract

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

References in corpus (4)

• Information Invariance and Quantum Probabilities
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
• Bures-Hall Ensemble: Spectral Densities and Average Entropies

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• Bures-Hall Ensemble: Spectral Densities and Average Entropies
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• Skewness of von Neumann entanglement entropy
• Second-order statistics of fermionic Gaussian states
• Average capacity of quantum entanglement
• Entropy fluctuation formulas of fermionic Gaussian states
• From Rényi Entropy Power to Information Scan of Quantum States
• Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
• Entanglement capacity of fermionic Gaussian states
• Average mutual information for random fermionic Gaussian quantum states