Quantum correlations with no causal order

Details Quantum correlations with no causal order Quantum correlations with no causal order

2011-05-23

arxiv.org/abs/1105.4464v1

Physics

Quantum Physics

10 pages, 2 figures, 2 tables

Scientific paper

Much of the recent progress in understanding quantum theory has been achieved within an operational approach. Within this context quantum mechanics is viewed as a theory for making probabilistic predictions for measurement outcomes following specified preparations. However, thus far essential elements of the theory --- space, time and causal structure --- elude this operational formulation and are assumed to be fixed. Is it possible to extend the operational approach to quantum mechanics such that the notions of an underlying space-time or causal structure are not assumed? What new phenomenology can follow from such an approach? We develop a framework for multipartite quantum correlations that does not presume these notions, but simply that experimenters in their local laboratories can perform arbitrary quantum operations. All known situations that respect definite causal order, including signalling and no-signalling correlations between time-like and space-like separated experiments respectively, as well as probabilistic mixtures of these, can be expressed in this framework. Remarkably, we find situations where two experiments are neither causally ordered nor in a probabilistic mixture of definite causal orders. These correlations are shown to violate a causal inequality, enabling a communication task that is impossible if the operations are ordered according to a fixed background time. However, we show that classical correlations are always causally ordered, which suggests a deep connection between definite causal structures and classicality.

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