Matilde Baroni - Composable simultaneous purification: The signalling nature of non-signalling correlations

Composable simultaneous purification: The signalling nature of non-signalling correlations

This seminar, given by Matilde Baroni, will happend on 29 October 2025, at 13:0. It will take place in Room 25-26/ 105.

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Abstract

Purification theorems play a crucial role in quantum information, showing that mathematical models of quantum states and operations relate to physically realisable circuits. A long standing line of research has been concerned with the problem of finding appropriate conditions for simultaneous purification, allowing assemblages of quantum states or operations to be realised by equivalent circuits, up to measurements of auxiliary registers. One such result, the celebrated S-G-HJW theorem, resolves this question for quantum states, while the situation remains much less clear in the more general case of quantum operations. In this paper, we propose an operational no-signalling condition that generalises known simultaneous purification results to the case of quantum instruments. We proceed to show that this generalisation is well-behaved under sequential composition, composition along directed acyclic graphs, and composition with indefinite causal order. A further generalisation to quantum super-instruments allows us to further treat communication scenarios involving loops and players with internal states, thus establishing the equivalence of quantum correlations arising in multipartite space-like separated scenarios with a large class of multipartite communication scenarios admitting operational no-signalling. As a consequence, it follows that any interactive quantum realisation of non-signalling correlations outside of the quantum set must involve signalling communication.