Quantized Neighbourhoods

Details Quantized Neighbourhoods Quantized Neighbourhoods

2009-10-23

arxiv.org/abs/0910.4461v2

Physics

Quantum Physics

Superseded by arXiv:1012.1334

Scientific paper

Consider a set of physical systems, evolving according to some global dynamics yielding another set of physical systems. Such a global dynamics f may have a causal structure, i.e. each output physical system may depend only on some subset of the input physical system, whom we may call its "neighbours". We can of course write down these dependencies, and hence formalize them in a bipartite graph labeled with the physical systems sitting at each node, with the first (resp. second) set holding the global state of the composite physical system at time t (resp. t'), and the edges between the partition stating which physical systems may influence which. Moreover if f is bijective, then we can quantize just by linear extension, so that it now turns into a unitary operator Q(f) acting upon this set of, now quantum, physical systems. The question we address is: what becomes, then, of the dependency graph? In other words, has Q(f) got the same causal structure as f? The answer to this question turns out to be a surprising : No -- quantum information can in fact flow faster than classical information. Here we provide concrete examples of this, as well optimal bounds for the extent in which this can happen, asymptotically or not. These bounds are strongly related to the dependency graph of the inverse function.

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