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arXiv · 1510.06345

Indefinite causal structures for continuous-variable systems

Flaminia Giacomini·Esteban Castro-Ruiz·Časlav Brukner
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Abstract

In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum mechanics and general relativity may require a revision of this paradigm. The process matrix framework keeps the validity of quantum physics locally but does not assume the existence of a global causal order. It allows to describe causal structures corresponding to a quantum superposition of 'A is before B' and 'B is before A'. So far, the framework has been developed only for finite-dimensional systems, and a straightforward generalization to infinite dimensions leads to singularities. Such generalization is necessary for continuous-variable systems and is a prerequisite for quantum fields on indefinite causal structures. Here we develop the process-matrix framework for continuous-variable systems. We encounter and solve the problems of singularities. Moreover, we study an example of a process in infinite dimensions, and we derive correlations exhibiting intereference due to processes in which A is before B and B is before A.

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Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner. 2015-10-21. Indefinite causal structures for continuous-variable systems. https://doi.org/10.1088/1367-2630%2F18%2F11%2F113026

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