Figure 3. (a): $\tfrac{1}{2}{{ \mathcal I }}_{R}^{G}-{{ \mathcal E }}_{F,R}^{G}$ and (b): ${{ \mathcal I }}_{V}^{G}-{{ \mathcal E }}_{F,V}^{G}$ versus the parameters A and κ for η = 0.2. (a) shows the holding of the inequality $(1/2){{ \mathcal I }}_{\alpha }^{G}\geqslant {{ \mathcal E }}_{F,\alpha }^{G}$ via the Rényi-2 entropy (i.e. α = 2 ), while, (b) shows that even ${{ \mathcal E }}_{F,V}^{G}\geqslant {{ \mathcal I }}_{V}^{G}$ may happen, which supports the Hayden conjecture [40], and further evidences that the von Neumann entropy (i.e. α = 1) may not be the best choice for estimating entanglement in mixed TMGSs
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