Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

Abstract

We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone bootstrap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the "line-tension picture," motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational

Entanglement wedge cross-section in shock wave geometries

“…For localized shocks, however, we find an interesting behaviour in which the entanglement wedge cross-section settles at some non-zero value sometime before mutual information goes to zero. This results in a plateau, similar to the one observed in [44]. We show that at high temperatures this behaviour can be precisely captured by the line-tension picture [49][50][51][52][53][54][55], which was very recently extended to the local operator quenches in [56].…”

“…In particular, there is clear replica trick prescription 1 which can be used to compute it. This has been used in recent works to investigate the dynamical properties of reflected entropy in holographic CFTs [41] 2 as well as in more general CFTs [44,45]. For our purposes, however, it will be sufficient to know that reflected entropy [15] (or holographic entanglement of purification [36]) between two intervals [z…”

Time dependence of reflected entropy in rational and holographic conformal field theories

“…Note added. Similar calculations of the time dependence of the reflected entropy are performed in an independent work [40] that appeared on arXiv simultaneously with the first version of this paper.…”

Including contributions from entanglement islands to the reflected entropy

“…IV. The reflected entropy is known to be a correlation measure that includes contributions from both classical and quantum correlations [23,25,26,53]. However, there is not a general understanding of the precise kind of correlations quantified by the reflected entropy and also no general classification of multipartite entanglement.…”