On the quantum KKL theorem and related inequalities

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• Haonan Zhang, University of South Carolina
• Friday 29 November 2024, 12:30-13:30
• MR15.

If you have a question about this talk, please contact Subhayan Roy Moulik.

The KKL theorem is a fundamental result in Boolean function analysis, stating that any Boolean function has an influential variable. Montanaro and Osborne proposed a quantum extension of Boolean functions. In this context, some classical results have been extended to the quantum setting, such as Talagrand’s L1 - L2 inequality. However, a quantum version of the KKL theorem seems to be missing, as conjectured by Montanaro and Osborne. In this talk, I will present an alternative answer to this question, saying that every balanced quantum Boolean function has a geometrically influential variable. This is based on joint work with Cambyse Rouzé and Melchior Wirth.

This talk is part of the CQIF Seminar series.

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