In this paper, we analyze whether quantum correlations between successive steps of evaporation can open any way to resolve the black hole information paradox. Recently a celebrated result in literature shows that `small' correction to leading order Hawking analysis fails to restore unitarity in black hole evaporation. We study a toy qubit model of evaporation allowing small quantum correlations between successive steps and verify the previous result. Then we generalize the concept of correction to Hawking state by relaxing the `smallness' condition. Our result generates a nontrivial upper and lower bound on change in entanglement entropy in the evaporation process. This gives us a quantitative measure of correction that would mathematically facilitate restoration of unitarity in black hole evaporation. We then investigate whether this result is compatible to the established physical constraints of unitary evolution of a state in a subsystem. We find that the generalized bound on entanglement entropy leads to significant deviation from Page curve. This leads us to agree with the recent claim in literature that no amount of correction in the form of Bell pair states would lead to any resolution to the information paradox.
We investigate quantum correlations between successive steps of black hole evaporation and investigate whether they might resolve the black hole information paradox. ‘Small’ corrections in various models were shown to be unable to restore unitarity. We study a toy qubit model of evaporation that allows small quantum correlations between successive steps and reaffirm previous results. Then, we relax the ‘smallness’ condition and find a nontrivial upper and lower bound on the entanglement entropy change during the evaporation process. This gives a quantitative measure of the size of the correction needed to restore unitarity. We find that these entanglement entropy bounds lead to a significant deviation from the expected Page curve.
The black hole information puzzle arises from a discrepancy between conclusions drawn from general relativity and quantum theory about the nature of the radiation emitted by a black hole. According to Hawking's original argument, the radiation is thermal and its entropy thus increases monotonically as the black hole evaporates. Conversely, due to the reversibility of time evolution according to quantum theory, the radiation entropy should start to decrease after a certain time, as predicted by the Page curve. This decrease has been confirmed by new calculations based on the replica trick, which also exhibit its geometrical origin: spacetime wormholes that form between the replicas. Here we analyse the discrepancy between these and Hawking's original conclusions from a quantum information theory viewpoint, using in particular the quantum de Finetti theorem. The theorem implies the existence of extra information,
W, which is neither part of the black hole nor the radiation, but plays the role of a reference. The entropy obtained via the replica trick can then be identified to be the entropy
S(R∣W) of the radiation conditioned on the reference
W, whereas Hawking's original result corresponds to the non-conditional entropy
S(R). The entropy
S(R∣W), which mathematically is an ensemble average, gains an operational meaning in an experiment with
N independently prepared black holes: For large
N, it equals the normalised entropy of their joint radiation,
S(R1⋯RN)/N. The discrepancy between this entropy and
S(R) implies that the black holes are correlated. The replica wormholes may thus be interpreted as the geometrical representation of this correlation. Our results also suggest a many-black-hole extension of the widely used random unitary model, which we support with non-trivial checks.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signalling, entanglement monogamy, and the equivalence principle. We here provide a quantum model for Hawking pair black hole evaporation within which these principles are all respected. The model does not involve exotic new physics, but rather uses quantum theory and general relativity. The black hole and radiation are in a joint superposition of different energy states at any stage of the evaporation process. In the particular branch where the black hole mass is 0, the radiation state is pure and one-to-one with the initial state forming the black hole. Thus there is no information loss upon full evaporation. The original Hawking's pair entanglement between infalling and outgoing particles gets transferred to outgoing particles via entanglement swapping, without violation of no-signalling or the entanglement's monogamy. The final state after the full black hole evaporation is pure, without loss of information, violation of monogamy, or the equivalence principle.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein–Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of 0 mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.
We investigate the multi-partite entanglement structure of an evaporating black hole and its Hawking radiation by dividing the radiation into finer subsystems. We approximate an evaporating black hole and its radiation with a Haar-random state for this purpose. Using the multi-entropy of these configurations, we define a black hole multi-entropy curve, which describes how the multi-entropy changes during the black hole evaporation. This black hole multi-entropy curve is a natural generalization of the Page curve since the multi-entropy reduces to the entanglement entropy for the bi-partite case. The multi-entropy curve keeps increasing in the early time. It reaches the maximum value at the multi-entropy time, which is later than the Page time, and starts to decrease. However, it does not decrease to zero at the end of the black hole evaporation. This non-zero value of the multi-entropy represents the secret entanglement between Hawking particles.