Black Hole Entanglement Shuffles Correlations at the Scrambling Time, New Study Finds

Few puzzles in theoretical physics have proven as stubborn as the black hole information paradox, and few recent ideas have energized the field as much as the so-called island formula. Now, a new study in The European Physical Journal C by Anirban Roy Chowdhury, Souvik Paul and Sunandan Gangopadhyay of the S.N. Bose National Centre for Basic Sciences in Kolkata adds a striking twist to that story. The researchers show that when a black hole passes its Page time, quantum correlations do not simply appear or disappear in isolation. Instead, they appear to be redistributed across spacetime in a highly structured way: as one pair of regions loses all correlation, another pair becomes maximally entangled, and a third measure of entanglement reveals a genuinely multipartite pattern of information sharing.

To appreciate why this matters, it helps to recall the paradox itself. Stephen Hawking showed in the 1970s that quantum fluctuations near a black hole’s horizon create entangled pairs of particles, one of which escapes as Hawking radiation while its partner falls inward. A semiclassical analysis of this radiation suggests that its von Neumann entropy, a measure of quantum information, grows monotonically as the black hole evaporates. But a black hole formed from a pure quantum state should, by the rules of unitary quantum mechanics, produce radiation that ends in a pure state, with vanishing entropy. Hawking’s calculation says otherwise, implying that information is destroyed, a conclusion that clashes with the foundations of quantum theory.

Don Page reframed the problem in the 1990s with a curve that now bears his name. The Page curve tracks the entropy of the radiation over time: it should rise until the Page time, when the radiation entropy equals the black hole’s thermal entropy, and then fall back to zero as evaporation completes. The challenge for theorists was to derive the falling portion of this curve from first principles. That breakthrough arrived through the AdS/CFT correspondence and the concept of entanglement wedge reconstruction, which culminated in the island formula. This formula states that the fine-grained entropy of Hawking radiation equals the minimum, over candidate regions called islands, of the sum of the area of the island’s boundary, measured in units of Newton’s constant, and the ordinary von Neumann entropy of the matter fields on the island together with the radiation.

The island formula can be derived using the replica trick, in which multiple copies of the black hole system are glued together and the resulting gravitational path integral is evaluated. Two competing saddle points emerge. At early times, the Hawking saddle dominates, no island contributes, and the radiation entropy climbs exactly as Hawking predicted. After the Page time, a new saddle, the replica wormhole, takes over. The island, a region inside the black hole bounded by quantum extremal surfaces, begins to contribute, and the entropy of the radiation turns over, tracing the unitary Page curve. The new work builds on this framework but shifts attention to a different quantity: mutual information, which quantifies the total correlation, classical and quantum, between two subsystems.

In earlier papers, the same group showed that for an eternal black hole, the mutual information between two exterior regions, labeled B+ and B-, vanishes precisely at the scrambling time, the timescale over which black holes are believed to scramble information faster than almost any other physical system. This vanishing is not a curiosity. It forces the matter entropy appearing in the island formula to become time independent, and after extremization the resulting radiation entropy yields the correct Page curve in the post-Page time regime. The formalism was shown to hold for eternal black holes in asymptotically flat, de Sitter and anti-de Sitter spacetimes.

The new paper’s central discovery concerns what happens to correlations elsewhere on the same Cauchy slice, the spacelike surface on which all these regions live. The authors computed the mutual information between the island, denoted I, and the full radiation region R, the union of the two exterior segments R+ and R-. Remarkably, they found that this quantity can never vanish; the entanglement wedge connecting the island and the radiation is always in a connected phase. More striking still, under exactly the condition that drives the mutual information between B+ and B- to zero, namely when the difference of the boundary times equals the difference of the tortoise-coordinate radii, the mutual information between the island and the radiation diverges. The two regions become maximally entangled at precisely the moment the exterior regions become fully decoupled.

The researchers are careful to note that this divergence is physically meaningful rather than an artifact. Mutual information between disjoint regions is ultraviolet finite by construction, so the singularity does not stem from short-distance divergences in the individual entropies. Nor does it arise from bringing endpoints of the regions together. Instead, it follows directly from the scrambling-time condition, and numerical plots confirm the picture: as a parameter interpolating toward the scrambling time increases, the correlation between the exterior regions steadily falls to zero while the island-radiation correlation climbs without bound. The authors interpret this as a redistribution of geometric entanglement across the Cauchy slice, and they show that either of the two conditions, vanishing B+ and B- correlation or divergent island-radiation correlation, suffices to reproduce the correct Page curve, with both formulations yielding the same time-independent matter entropy inside the island formula.

The second major result is entirely new to the literature: an analytic computation of the tripartite mutual information among the island and the two radiation regions, a quantity that had resisted direct calculation. Tripartite information measures whether correlations are extensive, and its sign carries deep meaning. The authors derived an exact expression and showed, both analytically and graphically as a function of the island time and the observer’s time, that it is always negative. Negative tripartite information means the mutual information is superextensive and monogamous: entanglement between the island and one radiation sector cannot be shared with the other. In quantum information terms, the information stored in the island is encoded nonlocally across the two radiation sectors, so that part of it is accessible only through the joint correlations of R+ and R- together, not from either sector alone.

This monogamy result has evocative implications. It suggests that reconstructing the interior degrees of freedom of the black hole may require access to the combined radiation system, reflecting a genuinely multipartite, highly nonlocal encoding of information, a structure reminiscent of quantum error-correcting codes and consistent with the known monogamy of mutual information in holographic theories. The calculations were carried out in the tractable setting of Jackiw-Teitelboim gravity in two dimensions, coupled to a flat thermal bath and filled with a two-dimensional conformal field theory, the standard laboratory for island physics, where the dilaton field provides the nontrivial gravitational dynamics that pure two-dimensional Einstein gravity lacks.

The authors emphasize that their findings open a new route to the Page curve: rather than demanding that the two exterior regions decouple, one may equivalently demand that the island and the radiation become infinitely correlated, and both routes lead to the same unitary entropy evolution. Whether these conditions remain essential for evaporating, rather than eternal, black holes is left for future work, as is a detailed dynamical treatment. But the conceptual message is already provocative. At the scrambling time, the geometry of quantum information around a black hole appears to reorganize itself, draining correlation from one set of regions and concentrating it, without limit, in another, while the entanglement that remains is locked away in monogamous, multipartite form. In that redistribution may lie a clue to how spacetime itself stores the information that Hawking’s calculation seemed to lose.

Subject of Research: Mutual information and tripartite entanglement in the island approach to the black hole Page curve

Article Title: New insights on mutual information in the island approach to the Page curve

Article References: Chowdhury, A. R., Paul, S., & Gangopadhyay, S. (2026). New insights on mutual information in the island approach to the Page curve. The European Physical Journal C, 86(9), Article 1031. https://doi.org/10.1140/epjc/s10052-026-16291-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16291-x

Keywords: black holes, information paradox, Page curve, island formula, mutual information, tripartite information, entanglement entropy, scrambling time, JT gravity, quantum extremal surfaces, replica wormholes, holography