  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.
