Information-theoretic Bell inequalities based on Tsallis entropy

We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities the Tsallis entropy is more suitable than the Shannon entropy, as it reveals nonclassicality for a larger set of quantum states. Finally, we find that, like probability-based inequalities, entropic ones are maximally violated by the non–maximally entangled qutrit state.

Figure 1

Maximal inequality violations as a function of $\beta$ for fixed Tsallis parameter $q=1.5$.

Figure 2

Maximal inequality violations as a function of $q$ for fixed $\beta =0$.

Figure 3

Dependence of visibility $V_c$ on Tsallis parameter $q$ for $\beta =1$. The relation is the same for metrics (2), (4), and (5).

Figure 4

Dependence of visibility $V_c$ on Tsallis parameter $q$ for $\beta =0$.