Holographic entanglement negativity and replica symmetry breaking

We evaluate the entanglement wedge cross section (EWCS) in asymptotically AdS geometries which are dual to boundary excited states. We carry out a perturbative analysis for calculating EWCS between the vacuum and other states for a symmetric configuration consisting of two disjoint strips and obtain analytical results in the specific regimes of the parameter space. In particular, when the states described by purely gravitational excitations in the bulk we find that the leading correction to EWCS is negative and hence the correlation between the boundary subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. Our study reveals some generic properties of boundary information measures dual to EWCS, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.

mentioning

confidence: 99%

Entanglement wedge cross section in holographic excited states

Sahraei

Vasli

Mozaffar

et al. 2021

“…This is in contrast to the holographic theories where the negativity is proportional to the mutual information for all times, i.e. E = 3I/4 [20] or E = I/2 [30]. Moreover, in the decompactification limit (increasing the system and subsystem sizes properly) the rate of decreasing of logarithmic negativity becomes more sharply which it might be the sign of sudden death of entanglement before the trivial (finite size effect) revival.…”

Section: Ln Vs Mutual and 1/2-rényi Mutual Informationmentioning

confidence: 73%

“…Although, it has been recently argued that there might be counterexamples for this duality; for more details see[30] 4. Recently, OEE for Lifshitz scalar theories has been studied in[31] where it has been shown that it can be negative.…”

mentioning

confidence: 99%

Odd entanglement entropy and logarithmic negativity for thermofield double states

Ghasemi

Naseh

Pirmoradian

2021

We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times t < β/2 (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times t < d/2 (half of the distance between intervals). We also find a similar delay to see linear growth of ∆S = SOEE− SEE. All these results show that the dynamics of these measures are consistent with the quasi-particle picture, of course apart from the logarithmic growth.

“…So long as the minimal extremal surface homologous to U is unique, and we restrict to n < O(1/G N ), this remains true in the stateψ. 10 Given this, the additional qubits do not enter E U in the perturbed state, so do not contribute their entropy to S(U )ψ. On the other hand, by the unitarity property the message is localized to V 1 ∪ U , so the entropy of the additional n qubits do contribute to S(V 1 U )ψ.…”

Section: Jhep09(2021)042mentioning

confidence: 99%

“…In the context of the AdS/CFT correspondence, the Ryu-Takayanagi formula [1] and its covariant generalizations [2][3][4][5] have deepened our understanding of how geometry and gravitational physics can be recorded into quantum mechanical degrees of freedom. Other proposals relate a variety of bulk geometric quantities to boundary entanglement, see [6][7][8][9][10] for an incomplete listing. In all cases, boundary correlation is related to bulk spacelike surfaces.…”

Section: Introductionmentioning

confidence: 99%

Bulk private curves require large conditional mutual information

May

2021

We prove a theorem showing that the existence of “private” curves in the bulk of AdS implies two regions of the dual CFT share strong correlations. A private curve is a causal curve which avoids the entanglement wedge of a specified boundary region $$ \mathcal{U} $$ U . The implied correlation is measured by the conditional mutual information $$ I\left({\mathcal{V}}_1:\left.{\mathcal{V}}_2\right|\mathcal{U}\right) $$ I V 1 : V 2 U , which is O(1/GN) when a private causal curve exists. The regions $$ {\mathcal{V}}_1 $$ V 1 and $$ {\mathcal{V}}_2 $$ V 2 are specified by the endpoints of the causal curve and the placement of the region $$ \mathcal{U} $$ U . This gives a causal perspective on the conditional mutual information in AdS/CFT, analogous to the causal perspective on the mutual information given by earlier work on the connected wedge theorem. We give an information theoretic argument for our theorem, along with a bulk geometric proof. In the geometric perspective, the theorem follows from the maximin formula and entanglement wedge nesting. In the information theoretic approach, the theorem follows from resource requirements for sending private messages over a public quantum channel.