n-partite information in Hawking radiation

Finiteness of entanglement entropy in a quantum black hole

“…We remark that this regularized term is now finite at the limit ǫ → 0 or β → ∞. The regularized one-partite information I [1] = −∆S ′ div also becomes finite at limit M → ω. We compare the behavior of ( 2) and ( 14) in the Fig.…”

“…The central charge c encodes the degrees of freedom in the field theory, while the constant of proportionality α could depend on species and spins of radiated particles [10]. These similarities between (2) and (4) as summarized in the Table I, have made us propose a (0 + 1)−dimensional quench model such that a massive radiated particle comes in sudden entangled with a black hole of mass M would carry the entanglement entropy S E ∼ ln(M/m p ) at late time [1]. In fact, the entropy difference (3) agrees with the definition of one-partite information in our quench model and the two-partite information are closely related to the definition of mutual information in the Parikh-Wilczek tunneling model [11][12][13].…”

“…It is tempted to think that this finite quantity associates with the information leakage via its radiation. The one-partite information could be defined as the loss of entropy, that is I [1] = −∆S div [1]. It grows exponentially at later stage of evaporation, as shown in the figure 1.…”

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A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed in the [1] to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for n-partite quantum information. However, this preliminary form suffers from the notorious divergence at its low temperature limit.

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“…where indexes p, s, t, u, • • • run through 1, 2, • • • , n. It has been shown that the n-partite information is always positive for even n and negative for odd n [1].…”