Quantumness of correlations in fermionic systems

We present an approach for the quantification of quantumness of correlations in fermionic systems. We study the multipartite relative entropy of quantumness in such systems and show how the symmetries in the states can be used to obtain analytical solutions. Numerical evidence of the uniqueness of such solutions is also presented. Supported by these results, we show that the minimization of the multipartite relative entropy of quantumness, over certain choices of its mode multipartitions, reduces to the notion of quantumness of indistinguishable particles. By means of an activation protocol, we characterize the class of states without quantumness of correlations. As an example, we calculate the dynamics of quantumness of correlations for a purely dissipative system, whose stationary states exhibit interesting topological nonlocal correlations.

Figure 1

Activation protocol for an $L$-mode system.

Figure 2

Dissipative evolution for a system with $L=4$ sites and $N=2$ particles, considering an initially uncorrelated single-Slater-determinant state (57). We show the time evolution for the quantumness of correlation of the state (${\mathcal{Q}}_p^{\varnothing }$), its purity $\left[\text{Tr}\left({\rho }^2\right)\right]$, and its entanglement according to the shifted negativity [11] and concurrence [5] quantifiers.

Figure 3

(a) Probability distribution for the quantumness of correlations in the sampled space to $E_{\mathrm{par}}$. We use a sample space of $\sim {10}^5$ quantum states. Also shown is the $T_E(\varphi ,\theta )$ function for the (b) $E_{\mathrm{par}}^{\left(1\right)}$ and (c) $E_{\mathrm{par}}$ ensembles.