We study various scaling behaviors of n-partite information during a process of thermalization for n disjoint system consisting of n parallel strips whose widths are much larger than the separation between them. By making use of the holographic description for entanglement entropy we explore holographic description of the n-partite information by which we show that it has a definite sign: it is positive for even n and negative for odd n. This might thought of as an intrinsic property of a field theory which has gravity dual.
Abstract We study operator entanglement measures of the unitary evolution operators of (1 + 1)-dimensional conformal field theories (CFTs), aiming to uncover their scrambling and chaotic behaviors. In particular, we compute the bi-partite and tri-partite mutual information for various configurations of input and output subsystems, and as a function of time. We contrast three different CFTs: the free fermion theory, compactified free boson theory at various radii, and CFTs with holographic dual. We find that the bi-partite mutual information exhibits distinct behaviors for these different CFTs, reflecting the different information scrambling capabilities of these unitary operators; while a quasi-particle picture can describe the case of the free fermion and free boson CFTs well, it completely fails for the case of holographic CFTs. Similarly, the tri-partite mutual information also distinguishes the unitary evolution operators of different CFTs. In particular, its late-time behaviors, when the output subsystems are semi-infinite, are quite distinct for these theories. We speculate that for holographic theories the late-time saturation value of the tri-partite mutual information takes the largest possible negative value and saturates the lower bound among quantum field theories.
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.