# quantum causal structure

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We take causal structure to be some relation defined over elements which are understood to be morphisms of some category. An example of such a relation is a domain, another is a directed acyclic graph. Yet another is a string diagram in a symetric monoidal category. Panangaden and Martin showed that interva domains are categorically equivalent to (hyperbolic?) spacetimes. This makes the domain a perfect candidated for clsssical relativistic causality. The planar graphs of the diagrammatical calculus are an enticing candidated for quantum causal structure. Then there is Hardy's causaloid. The classical causal structure seems very realist, as in we might believe in the existence of the set of events for a universe. I have offered the Fischer Impossibility result as a refutation of the naïve existence of this set.
What are the best candidates for a quantum causal structre?

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asked Nov 25, 2011
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Why shouldn't the quantum causal structure be identical to the classical causal structure? Are you worried about quantum gravity and information escaping from black holes? Or are you worried about entanglement affecting causality? And why should the Fischer Impossibility result be related to either of these questions?

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I don't understand what you mean by quantum causal structure. Quantum mechanics is non-signalling so causal structure is the same as in the classical case.

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@Joe: The question of causal structure with respect to quantum gravity and black holes is, as far as I am concerned, wide open. However, this question seems to me to have thrown together a paper related to quantum gravity (Hardy's causaloid), a paper on the connection between classical general relativity and a continuous analog of posets (Panangaden and Martin), a mention of the diagrammatic calculus which is too vague to tell exactly what is meant, and what strikes me as a completely unrelated theorem from distributed computing (Fischer). I'm voting to close as not a real question.

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@Peter: Sorry Peter, I was referring to the original question, not your comment. I don't dispute that the quantum gravity case is open, but we know so little about that area that it is hardly surprising that it is open. I know some of the results the question refers to, but can't make much sense of what the poster has in mind. I'll cast a virtual vote to close, but since my vote is binding, I won't actually close the question yet. I'd like to give the OP time to actually explain what they mean. If nothing happens in a few days, I'll kill the question.

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@Joe: no apology needed. I agree we should give the poster time to explain his question better (although if the question does get closed before he has time to revise it, it can always be reopened).

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You can use fIscher impossibility to show that consensus over the set of all processes, ie a notion of a universe, is untenable as it is a direct analogue of group consensus. This is when working under the assumption of a universe of discrete events with a causal structure. We see computer crashes like falling into a black hole. I wrote about that here: http://www.cs.mcgill.ca/~bsprot1/EvolvingUniverseFeb24.pdf

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It is natural to consider different kinds of causal structure. I see the classical causal structure as having more to do with the causal diagrams which we can readily observed of an apparatus. But more and more research these days is demonstrating that apparata are likely classical structures in a quantum category like a categeory of comonoids in a monoidal category.

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## 1 Answer

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It seems the FLP impossibility result may not hold for quantum systems (see this paper by Helm and section 5 of this paper for a criticism of the first), in which case you don't need any exotic causal structure for quantum mechanics to avoid it.

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answered Nov 26, 2011 by (3,575 points)
in this paper http://arxiv.org/abs/0903.1133 (section 5) is claimed that Helm results are correct but, (quote) *"due to the modiﬁcation of initialization of the system, and not to quantum mechanics."*

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@lurscher: Good catch. I'm not really sure where things stand then. I've updated my answer to include the reference in your comment.

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