Parallel repetition of entangled games via the superposed information cost

Parallel repetition of entangled games via the superposed information cost

Seminar author:Andrè Chailloux

Event date and time:11/04/2014 03:00:pm

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In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value w*(G) of a game G is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs.
The n-fold parallel repetition Gn of G consists of n instances of G where Alice and Bob receive all the inputs at the same time and must produce all the outputs at the same time. They win Gn if they win each instance of G.
The main result presented in this talk is that for any free game G (meaning on a product distribution), the quantity w*(Gn) decreases exponentially in n. I will also present some improved parallel repetition theorem in the case of free projection games. To prove this parallel repetition, the concept of Superposed Information Cost for entangled games is used which is inspired from the information cost used in communication complexity.