Escape of quantum information across an analogue black hole horizon

TL;DR

Addressing black hole information paradox, the paper uses an analogue horizon realized in an XY spin chain with spatially varying couplings to simulate information transfer across a horizon. It derives Page-curve-like evolution of the entanglement entropy with a Page time $t_P$, and demonstrates transfer of interior entanglement and coherence to the exterior bath via radiation, with transport dependent on the initial interior state. The results provide a concrete quantum-simulation framework that links many-body dynamics to black hole information paradox notions, offering a testbed for how information might escape horizons in unitary quantum dynamics.

Abstract

The complete evaporation of black holes, as a natural endpoint of Hawking radiation, gives rise to the black hole information paradox, which fundamentally challenges the principles of unitarity and information conservation in quantum mechanics. Although the AdS/CFT correspondence indicates that information is preserved during black hole evaporation, the precise mechanism by which it is recovered from the Hawking radiation remains an open question. To explore a potential resolution, we investigate information transfer in an analog black hole spacetime realized through position-dependent coupling in an XY spin chain. We derive and demonstrate Page curve-like behavior, and analyze the transmission of quantum resources, such as entanglement and coherence, across the effective horizon. Our results show that quantum resources initially localized within an interior subsystem can be transferred to the exterior via particle radiation through the horizon. This study provides a novel perspective from quantum simulation on how information may escape from black holes, thereby contributing to the further understanding of the black hole information paradox.

Figures (5)

• Figure 1: (a) Schematic of the black hole analogue, realized via an XY spin chain with site-dependent couplings $\kappa_n$. The coupling $\kappa$ undergoes a sign reversal between the interior and exterior regions, demarcating the effective horizon. (b) Cross-section of the $\kappa$ distribution and associated light-cone schematic for the one-dimensional black hole model employed herein. (c) Time evolution of the entanglement entropy $S_{ent}$ between the black hole interior and exterior during continuous particle radiation from the interior. The red dashed line represents the semiclassical Hawking radiation prediction, characterized by linear growth; the green solid line depicts the Page curve, which coincides with the semiclassical result in the early regime but, following the Page time $t_P$ (when roughly half the particles have leaked out), exhibits a downturn and monotonic decay to zero upon complete black hole evaporation.
• Figure 2: Upper panel: Evolution of the entanglement entropy $S_{ent}$ between the system and the bath in the black hole analogue. The different curves correspond to initial states prepared with varying degrees of entanglement inside the system. Lower panel: Time evolution of the particle number inside the system for the same set of initial states. The white circles mark, for each case, the time at which the particle number reaches half of its initial value.
• Figure 3: (a) Time evolution of the concurrence between two nearest neighbor qubits inside the system (sites 1 and 2). (b) Time evolution of the concurrence between the two outermost qubits in the bath (sites $L$-1 and $L$). In both panels, the first two qubits of the system are initialized with different degrees of entanglement, parameterized by $\alpha$. The numerical data are obtained for a chain of length $L=10$ and a discretization spacing $d=2$.
• Figure 4: Time evolution of coherence, quantified via the $l_1$-norm, for two distinct qubits: the first qubit at site 1 within the system (red traces) and the final qubit at site $L$ in the bath (green traces). Two initial configurations for the first qubit are contrasted: the excited state (square markers) and the maximally coherent state (circular markers), with all other qubits initialized in the spin-down state. Numerical results are obtained for a chain of length $L=10$ and discretization spacing $d=2$.
• Figure 5: Trajectories of quantum state evolution on the Bloch sphere. Panels (a) and (b) depict measurements on distinct qubits: site 1 in the system for (a) and site $L$ in the bath for (b). Two initial states for the first system particle are considered: the spin-up excitation $\ket{\uparrow}$ (marked by blue squares) and the coherent superposition $\ket{+}$ (marked by pink circles). The points on the Bloch sphere corresponding to these initial states are enlarged with the respective markers. Numerical results are obtained for a chain of length $L = 10$ and discretization spacing $d = 2$.