possibly $+\infty$,

[(ii)]{} they assign the value $0$ to all Slater determinant states,

[(iii)]{} they are monotone with respect to restriction of states,

[(iv)]{} they are additive over independent subsystems, and

[(v)]{} they are invariant under changes of the $1$-particle basis.

The sandwiched relative Rényi entropy $\widetilde{D}_{1/2}$ equals twice the negative logarithm of “fidelity," and the corresponding correlation functional $\widetilde{\mathfrak{C}}_{1/2}$ is the “new measure" of correlation we proposed in Ref. [@GottliebMauser2005].

Special properties of nonfreeness {#Special properties of nonfreeness}
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Due to its definition in terms of von Neumann entropy, nonfreeness has some intuitively appealing properties that the other relative-entropy-type correlation functionals do not share.

The nonfreeness of a many-fermion density operator $\Delta$ has been defined to be its entropy relative to the associated free state $\Gamma_\Delta$. Prop. \[max ent prop\] states that the nonfreeness of $\Delta$ equals the difference between the von Neumann entropies of $\Gamma_\Delta$ and $\Delta$. The nonfreeness $\Cor(\Delta)$ may be defined without direct reference to $\Gamma_\Delta$, by $$\Cor(\Delta) \equals \min \big\{S(\Delta\|\Gamma ) : \ \Gamma  \ \hbox{is free} \big\}$$ because the minimum relative entropy is actually attained at $\Gamma=\Gamma_{\Delta}$, as shown in Prop. \[superproposition\] below.

Simple formulas for nonfreeness {#Simple formulas for nonfreeness}
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Recall that 