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Stability for projection-valued measures and applications to nonlocal games

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OGGW04 - Stability and probabilistic methods

We will discuss reductions from synchronous nonlocal games to independent set games on graphs. This was first done for perfect strategies by Mančinska, Roberson, and Varvitsiotis, and we will show how to use a new stability theorem to lift this result to approximate strategies. This yields a so-called gap-preserving reduction, with further implications towards the complexity of deciding the quantum value of independent set games. We will discuss how our theorem fits in the larger framework of stability results, as well as some necessary background, connections to quantum information theory, and a sketch of the proof. This talk is based on joint work with Laura Mančinska, Taro Spirig, and Matthijs Vernooij.

This talk is part of the Isaac Newton Institute Seminar Series series.

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