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A<sc>bstract</sc> The entanglement negativity$$ \mathcal{E} $$ $E$(A:B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$generically break theℤ_2kreplica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumedℤ_2kreplica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$indeed break theℤ_2kreplica symmetry. Our argument involves an identity relating$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$to thek-th Rényi entropy on subregionAB^∗in the doubled state$$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ ${\left(,{\rho }_{\mathrm{AB}}\right)}_{A{A}^{\ast }{\mathrm{BB}}^{\ast }}$, from which we see that theℤ_2kreplica symmetry is broken down toℤ_k. Fork< 1, which includes the case of$$ \mathcal{E} $$ $E$(A:B) atk= 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for$$ {\mathcal{E}}^{(2k)} $$ $E^{\left(2k\right)}$and show that it is given by a new saddle with multiple cosmic branes anchored to subregionsAandBin the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations neark= 1. Moreover, we argue that theℤ_2ksymmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity. 

A<sc>bstract</sc> We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi indexn≥ 1, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. Forn <1, however, our proposal predicts a new phase with leading order (in Newton’s constantG) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: forn <1, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to then <1 Renyi entropies. 

A<sc>bstract</sc> We explore a large class of correlation measures called theα−zRényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, theα−zRMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values ofαandz, theα−zRMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute theα−zRMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography. 

A<sc>bstract</sc> We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined att= 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, aftert= 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics. 

A bstract While recent progress in the black hole information problem has shown that the entropy of Hawking radiation follows a unitary Page curve, the quantum state of Hawking radiation prior the Page time is still treated as purely thermal, containing no information about the microstructure of the black hole. We demonstrate that there is significant quantum information regarding the quantum state of the black hole in the Hawking radiation prior to the Page time. By computing of the quantum fidelity in a 2D boundary conformal field theory (BCFT) model of black hole evaporation, we demonstrate that an observer outside of an evaporating black hole may distinguish different black holes via measurements of the Hawking radiation at any time during the evaporation process, albeit with an exponentially large number of measurements. Furthermore, our results are universal, applicable to general BCFTs including those with large central charge and rational BCFTs. The techniques we develop for computing the fidelity are more generally applicable to excited states in CFT. As such, we are able to characterize more general aspects of thermalization in 2D conformal field theory.