# Table 2 Summary of results.

Quantum Classical Quantum Quantum Classical
Limit (no limit) (no limit) (dn) (dn 1) (dn 1)
ΔSinfo $$2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d\,-\,1\\ n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)$$ $$2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d\,-\,1\\ n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)$$ $$\approx\!2n\,{\mathrm{ln}}\,2$$ $$\approx \!2n\,{\mathrm{ln}}\,2$$
ΔSigno $${\sum }_{J}{p}_{J}{\mathrm{ln}}\,{d}_{J}^{B}\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)$$ $${\mathrm{ln}}\,\left(\begin{array}{c}2n\,+\,d\,-\,1\\ 2n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)$$ $$\approx\!{{\Delta }}{S}_{\text{info}}\,-\,H({\bf{p}})$$ $$\approx\!2n\,{\mathrm{ln}}\,2$$ ≈ 0
1. Entropy changes ΔSinfo, ΔSigno for the informed and ignorant observers and their limits are expressed for bosons with n = m. For fermions, replace the dimension of the symmetric subspace $$\left(\begin{array}{c}n\,+\,d\,-\,1\\ n\end{array}\right)$$ with that of the antisymmetric one $$\left(\begin{array}{c}d\\ n\end{array}\right)$$ and $${d}_{J}^{B}$$ by $${d}_{J}^{F}$$ (both of which are defined in Eq. (13)).