One-Shot Decoupling and Page Curves from a Dynamical Model for Black Hole Evaporation

Abstract

One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile that follows Page's prediction. We argue that information transfer and the emergence of Page curves is a robust feature of any multilinear interaction Hamiltonian with a bounded spectrum.

Tensor network models of unitary black hole evaporation

“…Thus, the averaged general invariants (12) are identical in all such models, regardless of our choice of I n .…”

“…1 In the past, various authors (see e.g. [3,4,5,6,7,8,9,10,11,12,13]) have studied toy models of black hole evaporation, in which a quantum system with Hilbert space H BH ⊗H rad evolves unitarily, with information from the black hole subsystem H BH being transferred somehow to the radiation subsystem H rad . In these models, various conditions are imposed on the dynamics in order to incorporate physical features expected of black hole evaporation.…”

Spontaneous parametric down conversion with a depleted pump as an analogue for black hole evaporation/particle production

“…Hence, further refinements than simply considering their maximum contribution from j i = k are warranted, yet difficult to implement analytically due to the large number of temporally ordered nested sums. Thus, it appears that some blend of an analytical approach detailed here, coupled with a numerical approach, as advocated by the lattice path method Brádler and Adami [3] might prove fruitful in gaining further physical insight the nature of the one-shot decoupling bipartite state |Ψ(N ) , and subsequently the detailed nature of the Page information of the Hawking radiation from an evaporating BH.…”

“…As such, the next generated pair does not interact with the previously generated pairs, and is coherent only with the BH internal degrees of freedom for a time on the order of average time between emission events. This is what the one-shot decoupling model of Brádler and Adami [3] seeks to capture.…”

“…In a recent paper, Bràdler and Adami [3] have expanded upon the work Nation and Blencowe [1] and Alsing [2] and developed a one-shot decoupling model for BH evaporation, in which the quantized modes of the BH are emitted sequentially in time into the out-going and infalling radiation modes [21]. The authors use the method of lattice paths to compute the von Neumann entropy of the reduced density matrix for the BH and show that its resulting time evolution is again qualitatively similar to that predicted by Page, in which information emerges from the BH at a time when the BH has evaporated to roughly half its initial size (population).…”