Do black holes create polyamory?

Abstract

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. A particular example of this is the Horowitz-Maldacena proposal, and we argue that it needn't lead to cloning or violations of entanglement monogamy. For measurements on systems which appear to be leaving a black hole, we introduce the notion of the temporal product, and argue that it is just as natural a choice for measurements as the tensor product. For black holes, the tensor and temporal products have the same measurement statistics, but result in different type of non-monogamy of correlations, with the former being forbidden in quantum theory while the latter is allowed. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tame violation of entanglement monogamy.

20 pages, comments welcome, grants added to acknowledgements

References in corpus (5)

• Jerusalem Lectures on Black Holes and Quantum Information
• Inferring causal structure: a quantum advantage
• Monogamy of Bell correlations and Tsirelson's bound
• Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle
• Comment on "Measurements without probabilities in the final state proposal"

Cited by in corpus (5)

• Comment on "Measurements without probabilities in the final state proposal"
• On local conservation of information content in Schwarzschild black holes
• Binary Black Hole Information Loss Paradox & Future Prospects
• Quantum black holes as solvents
• Tsirelson's Bound and the Quantum Monogamy Bound from Global Determinism