##### Department of Mathematics,

University of California San Diego

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### Math 243, Functional Analysis

## Prof. Bill Helton

#### UC San Diego

## Perfect quantum strategies for XOR games

##### Abstract:

The talk will describe some of the structure associated with 'perfect quantum strategiesâ€™ for a class of cooperative games. In such problems one has a (noncommutative) algebra A which encodes quantum mechanical laws and a list of matrix equations. A solution to these amounts to a perfect quantum strategy; 1 x 1 matrix solutions give a perfect classical strategy. The focus will be on 3XOR games. There is now a way to determine if a perfect quantum strategy exists and construct it if it does. The core of the construction is a variant on the classical 3XOR SAT problem. The talk will describe current understanding of this variant, in particular the sharp transition between solvability and unsolvability as numbers of constraints vs unknowns vary. The work is joint with Adam Bene Watts, Zehong Zhao, Jared Huges and Daniel Kane.

Host:
Priyanga Ganesan

### February 20, 2024

### 11:00 AM

APM 7218 and** **Zoom (meeting ID: 94246284235)

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