Tsallis entropy and q-analogue of information

Angel Ricardo Plastino, Angel Ricardo Plastino

Qi Han, Shuai Wang, Lijie Gou +1 more

M. Portesi, Angel Ricardo Plastino, F. Pennini

Boaz Tamir

In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information theory. Similarly we redefine entropy exchange and use the same bound.

Satish Kumar, Arun Choudhary

In this paper we define some new generalized measures of ‘useful’ relative information and study their particular cases. We also obtain their relations with common entropy measures. Moreover, we define the quantum generalized Tsallis entropy and show that projective measurement does not decrease the quantum generalized Tsallis entropy of a quantum state. Finally, we define generalized quantum Tsallis and Renyi relative entropies and discuss their particular cases.

Lu Wei

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the 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 proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.