Composable simultaneous purification: when all communication scenarios reduce to spatial correlations

• URL: http://arxiv.org/abs/2601.05158v1
• Date: Thu, 08 Jan 2026 17:48:56 GMT
• Title: Composable simultaneous purification: when all communication scenarios reduce to spatial correlations
• Authors: Matilde Baroni, Dominik Leichtle, Ivan Šupić, Damian Markham, Marco Túlio Quintino,
• Abstract summary: Non-signalling state assemblages can always be simultaneously purified.<n>We extend this simultaneous purification inspired result to all multipartite communication schemes.<n>Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set.
• Score: 1.4788776577018314
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bell non-locality is a powerful framework to distinguish classical, quantum and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication? Non-signalling state assemblages, and the fact that they can always be simultaneously purified, turned out to be the key element to restrict the simplest bipartite communication scenario, the prepare-and-measure, to the standard bipartite Bell scenario. Yet, many distinctive features of quantum theory are genuinely multipartite and cannot be reduced to two-party behaviour. In this work we are interested in extending this simultaneous purification inspired result to all multipartite communication schemes. As a first step, we unify and extend the simultaneous purification result from states to instruments and super-instruments, which are composable structures, and open up the possibility to explore more complex communication scenarios. Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set. As a consequence, any interactive quantum realization of correlations outside of this set must involve at least one signalling assemblage of quantum operations, even when the resulting correlations are non-signalling.

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