A bstract We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT 2 ) in a black hole background. The bulk dual is described by an AdS 3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT 2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.A bstract We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT 2 ) in a black hole background. The bulk dual is described by an AdS 3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT 2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

arXiv:2311.17023Journal of High Energy PhysicsMay 6, 202414 citations

Black holes and quantum coherence

Robert M. Wald

Foundations of PhysicsMay 1, 19862 citations

Entanglement and firewalls in quantum circuit model of black hole evaporation

Y S Lü, Tien Hsieh, Da-Shin Lee

Abstract We reexamine the quantum circuit model of black hole evaporation proposed in a previous work (Class. Quantum Grav. 35, 235013, 2018) [1]. This tripartite model incorporates the following systems: black hole ( $\textbf{BH}$ BH ), just radiation ( $\textbf{JR}$ JR ), and early radiation ( $\textbf{ER}$ ER ). We apply a scrambling unitary matrix with a single parameter $\theta$ θ to the ground state of the qubits in infalling matter toward a black hole in order to generate initial qubit states of the black hole that are more general than those in [1]. Specifically, the scrambling unitary matrix reduces to no scrambling and maximum scrambling when $\theta =0$ θ = 0 and $\theta =\pi /2$ θ = π / 2 , respectively. Our aim is to explore the role of quantum monogamy in the firewall formation between the black hole and radiation. In this model, entanglement and firewall formation depend on the black hole mass M and the frequency of Hawking radiation $\omega$ ω . For the initial state with $\theta =\pi /2$ θ = π / 2 , a firewall emerges at an earlier stage of the evolution than with $\theta =0$ θ = 0 . We also find that a firewall structure emerges between $\textbf{BH}$ BH and $\textbf{JR}$ JR , and that the information is carried away by radiation for all values of $M\omega$ M ω , provided that $\theta$ θ lies within a certain analytically determined range. Following unitary gate dynamics, the initial black hole qubit state can be retrieved from its imprint on the final radiation state, which was originally hidden behind the black hole’s horizon. These results may provide insight into the properties of multipartite entanglement due to the different initial states in the evolution of a quantum circuit model for black hole evaporation.Abstract We reexamine the quantum circuit model of black hole evaporation proposed in a previous work (Class. Quantum Grav. 35, 235013, 2018) [1]. This tripartite model incorporates the following systems: black hole ( $$\textbf{BH}$$ BH ), just radiation ( $$\textbf{JR}$$ JR ), and early radiation ( $$\textbf{ER}$$ ER ). We apply a scrambling unitary matrix with a single parameter $$\theta $$ θ to the ground state of the qubits in infalling matter toward a black hole in order to generate initial qubit states of the black hole that are more general than those in [1]. Specifically, the scrambling unitary matrix reduces to no scrambling and maximum scrambling when $$\theta =0$$ θ = 0 and $$\theta =\pi /2$$ θ = π / 2 , respectively. Our aim is to explore the role of quantum monogamy in the firewall formation between the black hole and radiation. In this model, entanglement and firewall formation depend on the black hole mass M and the frequency of Hawking radiation $$\omega $$ ω . For the initial state with $$\theta =\pi /2$$ θ = π / 2 , a firewall emerges at an earlier stage of the evolution than with $$\theta =0$$ θ = 0 . We also find that a firewall structure emerges between $$\textbf{BH}$$ BH and $$\textbf{JR}$$ JR , and that the information is carried away by radiation for all values of $$M\omega $$ M ω , provided that $$\theta $$ θ lies within a certain analytically determined range. Following unitary gate dynamics, the initial black hole qubit state can be retrieved from its imprint on the final radiation state, which was originally hidden behind the black hole’s horizon. These results may provide insight into the properties of multipartite entanglement due to the different initial states in the evolution of a quantum circuit model for black hole evaporation.

arXiv:2606.21181The European Physical Journal CJul 26, 20260 citations

Reflected entropy for communicating black holes II: Planck braneworlds

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra +1 more

Abstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in finite-sized non-gravitating reservoirs described by $CFT_2$ C F T 2 s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by $AdS_2$ A d S 2 slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $AdS_3/CFT_2$ A d S 3 / C F T 2 correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.Abstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in finite-sized non-gravitating reservoirs described by $$CFT_2$$ C F T 2 s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by $$AdS_2$$ A d S 2 slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $$AdS_3/CFT_2$$ A d S 3 / C F T 2 correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.

arXiv:2302.12810The European Physical Journal CMar 9, 20246 citations

\textbf{BH}

BH ), just radiation (

\textbf{JR}

JR ), and early radiation (

\textbf{ER}

ER ). We apply a scrambling unitary matrix with a single parameter

\theta

θ to the ground state of the qubits in infalling matter toward a black hole in order to generate initial qubit states of the black hole that are more general than those in [1]. Specifically, the scrambling unitary matrix reduces to no scrambling and maximum scrambling when

\theta =0

θ = 0 and

\theta =\pi /2

θ = π / 2 , respectively. Our aim is to explore the role of quantum monogamy in the firewall formation between the black hole and radiation. In this model, entanglement and firewall formation depend on the black hole mass M and the frequency of Hawking radiation

\omega

ω . For the initial state with

\theta =\pi /2

θ = π / 2 , a firewall emerges at an earlier stage of the evolution than with

\theta =0

θ = 0 . We also find that a firewall structure emerges between

\textbf{BH}

BH and

\textbf{JR}

JR , and that the information is carried away by radiation for all values of

M\omega

M ω , provided that

\theta

θ lies within a certain analytically determined range. Following unitary gate dynamics, the initial black hole qubit state can be retrieved from its imprint on the final radiation state, which was originally hidden behind the black hole’s horizon. These results may provide insight into the properties of multipartite entanglement due to the different initial states in the evolution of a quantum circuit model for black hole evaporation.

CFT_2

C F T 2 s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by

AdS_2

A d S 2 slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the

AdS_3/CFT_2

A d S 3 / C F T 2 correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.