On the monogamy of holographic $n$-partite information

We investigate the monogamy of holographic $n$-partite information for a system consisting of $n$ disjoint parallel strips with the same width and separation in AdS and AdS black brane geometries. More precisely, we study the sign of this quantity, e.g., for $n=4$, 5, in various dimensions and for different parameters. Our results show that for quantum field theories with holographic duals, the holographic 4-partite information is always positive, and the sign of holographic 5-partite information is found to be negative in the dual strongly coupled $1+1$ dimensional conformal field theory. This latter result indicates that the holographic 4-partite information is monogamous. We also find the critical points corresponding to the possible phase transitions of these quantities.

Figure 1

Schematic diagram of the holographic prescription of two different configurations for computing $S(A\cup B)$.

Figure 2

Holographic mutual information in $\mathrm{Ad}{\mathrm{S}}_3$ (left) and $\mathrm{Ad}{\mathrm{S}}_4$ (right) backgrounds for $\ell =1$, 2, 3, 4, 5 from left to right.

Figure 3

Schematic representation of RT surfaces corresponding to the possible configurations of minimal surfaces in computing holographic tripartite information.

Figure 4

Holographic tripartite information in $\mathrm{Ad}{\mathrm{S}}_3$ (left) and $\mathrm{Ad}{\mathrm{S}}_4$ (right) backgrounds for $\ell =1$, 2, 3, 4, 5 from left to right.

Figure 5

Schematic representation of RT surfaces corresponding to seven different configurations in computing the HEE of union four strips.

Figure 6

Holographic 4-partite information in $\mathrm{Ad}{\mathrm{S}}_3$ (left) and $\mathrm{Ad}{\mathrm{S}}_4$ (right) backgrounds for $\ell =1,2,3,4,5$ from left to right.

Figure 7

Schematic representation of the RT surfaces corresponding to 11 different configurations in computing the HEE of union five strips.

Figure 8

Holographic 5-partite information in $\mathrm{Ad}{\mathrm{S}}_3$ background for $\ell =1$, 2, 3, 4, 5 from left to right.

Figure 9

Left plot: Comparison of numeric HEE (blue) with semianalytic HEE for $\ell \ll {\rho }_H$ (red) in ${\mathrm{AdS}}_3\text{−}\mathrm{BH}$. Right plot: Comparison of numeric HEE (blue) with semianalytic HEE for $\ell \ll {\rho }_H$ (red) and $\ell \gg {\rho }_H$ (green) limits in ${\mathrm{AdS}}_4\text{−}\mathrm{BH}$.

Figure 10

Holographic $n$-partite information in ${\mathrm{AdS}}_3\text{−}\mathrm{BH}$ for $\ell =0.1,0.2,0.3,1,2$ from left to right.

Figure 11

Holographic 4-partite information in ${\mathrm{AdS}}_4\text{−}\mathrm{BH}$ for $\ell =0.1,0.2,0.3,0.4,0.5$ from left to right.