A controllable quantum spin chain model is introduced, reproducing the Page curve — the characteristic rise and fall of bipartite entanglement expected during black hole evaporation. Two interacting Ising chains in a transverse field are used, forming a pure bipartite state. The process of Hawking evaporation is simulated by dynamically shrinking the ‘system’ chain and growing the ‘environment’ chain; the unitary real-time evolution is modeled with tensor networks in the matrix product state (MPS) representation. The hallmark Page curve profile robustly emerges under this controlled change in subsystem size and, remarkably, persists even with zero Hamiltonian coupling across the boundary, showing that merely shrinking the Hilbert space dimension can produce this behavior. The detailed shape of the curve is shown to depend on the internal information dynamics: at criticality the profile is smooth, while departing from criticality distorts the rise and fall of entanglement.
A diary loses pages, yet the story migrates to the rest. Black holes act similarly: as they shrink (shown by Stephen Hawking), swallowed information shouldn't vanish; it eventually resurfaces. Theory predicts a specific rise-and-fall curve for this escape.
Physicists built a miniature version with two strings of tiny magnets—one for the black hole, the other for the universe. Removing magnets one by one from the “black hole” string mimicked evaporation. They measured entropy—shared information—between the strings, and the pattern matched perfectly.
At a precise magnetic tipping point, like a compass needle quivering before it flips, the information streamed out smoothly. These chains fit inside current quantum computers, turning them into labs for testing how the cosmos handles its records.
🎯 The Page curve was first proposed by physicist Don Page in 1993, and he bet Stephen Hawking that information is not lost in black holes. Hawking conceded the bet in 2004.
🎬 In the movie Interstellar, the protagonist sends a message from inside a black hole using gravity, hinting that information can escape – a scenario now being probed by these quantum magnet models.