Characterizing quantum bilocal network scenario with generalized NPA hierarchies

IQC CS/Math Seminar - Xiangling Xu (Inria Saclay) ZOOM + QNC 1201

Characterizing quantum correlations is a fundamental task in the study of quantum information theory. In the standard Bell scenario, where the correlations are established by a single source, the seminal work [Navascúes et al., 2008] presents a convergent hierarchy that provides an outer approximation, which can be formulated as a problem solvable by computers.

In the more general networks scenarios, however, the correlations are due to multiple independent quantum sources. This necessitates a generalization of the NPA hierarchy. Based on [Renou, Xu, Ligthard, 2022], this talk focuses on the simplest quantum network, the bilocal scenario, where two independent quantum sources exist: one shared between Alice and Bob, and the other between Bob and Charlie. It will discuss two convergent generalizations of the NPA hierarchy in this context, demonstrating that the bilocal scenario is completely understood from the algebraic/Heisenberg perspective.

Despite this progress, the characterization of quantum networks beyond the bilocal scenario remains an open question. This talk will introduce a possible approach, the inflation-NPA hierarchy, as a potential solution. The aim is to motivate the audience to explore this important and challenging problem further.

https://uwaterloo.zoom.us/j/94060072976?pwd=HmYHDb7SDNv0h4n8LVnQNZ7etb8Psi.1

Passcode: 972236

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