We study multipartite entanglement in typical pure states holographically dual to pure BTZ black holes, using multientropy and its “genuine” version. In the bulk, these quantities are computed by minimal geodesic networks (so-called Steiner trees). We find that at sufficiently high temperature, the genuine tripartite multientropy exhibits a volume-law scaling in sharp contrast to vacuum AdS <inline-formula><tex-math id='TM0003' notation='LaTeX'>$_3$</tex-math></inline-formula>, where the genuine contribution is universal and size independent. Moreover, we find another phase: once one subsystem exceeds half of the total system, the leading genuine tripartite entanglement vanishes and reduces to that for global AdS <inline-formula><tex-math id='TM0004' notation='LaTeX'>${}_3$</tex-math></inline-formula>. This transition is indeed consistent with recent arguments for distillable Einstein&#8211;Podolsky&#8211;Rosen pairs in tripartite Haar-random states. Motivated by finite-cutoff holography, we further study the radial cutoff dependence of multientropy and show that genuine multientropy acquires nontrivial size dependence even for the tripartite case in AdS <inline-formula><tex-math id='TM0005' notation='LaTeX'>${}_3$</tex-math></inline-formula>. As a byproduct, we also observe an intriguing &#8220;area-law&#8221; contribution to multientropy that is relevant to vacuum AdS <inline-formula><tex-math id='TM0006' notation='LaTeX'>${}_3$</tex-math></inline-formula>.

Japan

Takanori Anegawa

Shota Suzuki

Kotaro Tamaoka

Black Holes as a Multipartite Entanglers: Multientropy in AdS 3/CFT 2

We argue that the special extremal slice inside an AdS black hole is dual to an absolutely maximally entangled (AME) state. We demonstrate this by confirming the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>-independence of holographic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>th Renyi entropies for any bipartite subsystems. Our result gives an AME state in an infinite-volume system, where the local bond dimension is set by the black hole entropy. In particular, our construction provides concrete support from the gravity side for the emergence of random structures and an infinite-dimensional Hilbert space in recent nonisometric holographic codes.

Holographic Absolutely Maximally Entangled States in Black Hole Interiors

We study quantum quench processes in (1+1)-dimensional conformal field theory (CFT) in which the initial thermal equilibrium (Gibbs) state is time-evolved by spatially inhomogeneous Hamiltonians, the so-called Möbius and sine-square-deformed (SSD) Hamiltonians. We found that, when the quench is induced by the SSD Hamiltonian, almost all the degrees of freedom are asymptotically gathered at a single point, resulting in a point-like excitation. This excitation, which we dub black hole-like excitation, carries as much information as the total thermal entropy. In contrast, other parts of the system approach the low-entropy (low-temperature) state at late times. For the quench by the Möbius Hamiltonian, we instead found an eternal periodic oscillation of physical quantities such as von Neumann entropy for subsystems. When the CFT admits a holographic dual description, the SSD quench induces a time-dependent, inhomogeneous deformation of the bulk black hole horizon, which, at late enough times, “touches” the boundary. Our quench setups can be used as a way to create low-temperature states, and, also, simulate the formation and evaporation processes of black holes.

Kanato Goto

China

Masahiro Nozaki

United States

Shinsei Ryu

Mao Tan

Non-equilibrating a black hole with inhomogeneous quantum quench

We study timelike and conventional entanglement entropy as potential probes of black hole singularities via the AdS/CFT correspondence. Using an analytically tractable example, we find characteristic behavior of holographic timelike entanglement entropy when the geometry involves a curvature singularity. We also observe interesting phenomena that, in some particular setups, holographic timelike and conventional entanglement entropy are determined from multiple complex saddle points, which fall outside the assumptions of the Lewkowycz-Maldacena type argument.

Black hole singularity and timelike entanglement

The thermodynamics and the entanglement properties of two-dimensional conformal field theories (2d CFTs) on curved backgrounds are studied. By means of conformal mapping we study the equivalent system on flat space governed by the deformed Hamiltonian, which is a spatial integral of the Hamiltonian density modulated by an enveloping function. Focusing on holographic CFTs, we observe Hawking-Page like phase transition for the thermal and the entanglement entropy as we vary the background metric. We also compute the mutual information to study the information theoretic correlation between parts of the curved spacetime. The gravity dual of 2d CFTs on curved background is also discussed.

Akihiro Miyata

Masataka Watanabe

Hawking-Page and entanglement phase transition in 2d CFT on curved backgrounds

We explore non-equilibrium processes in two-dimensional conformal field theories (2d CFTs) due to the growth of operators induced by inhomogeneous and homogeneous Hamiltonians by investigating the time dependence of the partition function, energy density, and entanglement entropy. The non-equilibrium processes considered in this paper are constructed out of the Lorentzian and Euclidean time evolution governed by different Hamiltonians. We explore the effect of the time ordering on entanglement dynamics so that we find that in a free boson CFT and RCFTs, this time ordering does not affect the entanglement entropy, while in the holographic CFTs, it does. Our main finding is that in the holographic CFTs, the non-unitary time evolution induced by the inhomogeneous Hamiltonian can retain the initial state information longer than in the unitary time evolution.

Weibo Mao

South Korea

Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians

The nonequilibrium process where the system does not evolve to the featureless state, that without quantum properties, is one of the new central objects in the nonequilibrium phenomena. In this paper, starting from the short-range entangled state in the two-dimensional conformal field theories (2D CFTs), the boundary state with a regularization, we evolve the system with the inhomogeneous Hamiltonians called Möbius/sine-square-deformed (SSD) ones. Regardless of the details of CFTs considered in this paper, during the Möbius evolution, the entanglement entropy exhibits the periodic motion called quantum revival. During SSD time evolution, except for some subsystems, in the large time regime, entanglement entropy and mutual information are approximated by those for the vacuum state. We argue the time regime for the subsystem to cool down to vacuum one is <math><msub><mi>t</mi><mn>1</mn></msub><mo>≫</mo><mi>O</mi><mo>(</mo><mi>L</mi><msqrt><msub><mi>l</mi><mi>A</mi></msub></msqrt><mo>)</mo></math>, where <math><msub><mi>t</mi><mn>1</mn></msub></math>, <math><mi>L</mi></math>, and <math><msub><mi>l</mi><mi>A</mi></msub></math> are time, system, and subsystem sizes. This finding suggests the inhomogeneous quench induced by the SSD Hamiltonian may be used as the preparation for the approximately vacuum state. We propose the gravity dual of the systems considered in this paper, furthermore, and generalize it. In addition to them, we discuss the relation between the inhomogeneous quenches and continuous multiscale entanglement renormalization ansatz (cMERA).

Mao Tian Tan

Inhomogeneous quenches as state preparation in two-dimensional conformal field theories

We study the dynamical properties of a strongly scrambling quantum circuit involving a projective measurement on a finite-sized region by studying the operator entanglement entropy and mutual information (OEE and BOMI) of the dual operator state that corresponds to this quantum circuit. The time-dependence of the OEE exhibits a new dynamical behavior of operator entanglement, namely an additional fractional coefficient that accompanies the linear time growth of the OEE. For a holographic system, this is equivalent to an additional fractional coefficient that modifies the linear growth rate of the wormhole volume. The time-dependence of the BOMI shows that the projective measurement may destroy the non-local correlations in this dual state. We also propose a gravity dual as well as a line-tension picture, which is an effective model, that describe this strongly scrambling quantum circuit.

Entanglement dynamics of the non-unitary holographic channel

Motivated by the quantum process of black hole evaporation and its implications for symmetries, we consider a qubit system with a random dynamics as a toy model of black hole. We compute its symmetry-resolved entropies and discuss its implications. We first consider the case where charges are conserved and compute the symmetry-resolved entropies. We derive a symmetry-resolved analogue of the Page curve. We then consider the case where symmetry is explicitly broken and charges are no longer conserved. It serves as a toy model for global symmetry breaking in black hole evaporation. Despite the simple framework, the symmetry-resolved entropies capture various interesting features during the analogous process of black hole evaporation in our qubit model.

Pak Lau

Toshifumi Noumi

Yuhei Takii

Page curve and symmetries

Abstract We study pseudo entropy for a particular linear combination of entangled states in qubit systems, two-dimensional free conformal field theories (CFTs), and two-dimensional holographic CFT. We observe phenomena whereby the pseudo entropy can be parametrically large compared with the logarithm of the dimension of the Hilbert space. We call these phenomena pseudo entropy amplification; it is analogous to the amplification of the weak value. In particular, our result suggests the holographic CFT does not lead to amplification as long as the non-perturbative effects are negligible. We also give a heuristic argument for when such (non-)amplification can occur.