Seminar: Professor Penghui Yao, Nanjing University
A doubly exponential upper bound on noisy EPR states for binary games
This seminar initiates the study of a class of entangled games, mono-state games, where the players in a non-local games are only allowed to share arbitrary copies of a given state.
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Presenter: Professor Penghui Yao, Nanjing University China
Title: A doubly exponential upper bound on noisy EPR states for binary games
Abstract:
This paper initiates the study of a class of entangled games, mono-state games, where the players in a non-local games are only allowed to share arbitrary copies of a given state. This paper provides a doubly exponential upper bound on the copies of for the players to approximate the value of the game to an arbitrarily small constant precision for any mono-state binary game, if the given state is a noisy EPR state, which is a two-qubit state with completely mixed states as marginals and maximal correlation less than 1. In particular, it includes an EPR state with an arbitrary positive depolarizing noise. The structure of the proofs is built on the recent framework about the decidability of the non-interactive simulations of joint distributions with significant extension, which is completely different from all previous optimization-based approaches or "Tsirelson’s problem"-based approaches. The paper develops a series of new techniques about the Fourier analysis on matrix spaces and proves a quantum invariance principle and a hypercontractive inequality for random operators. This novel approach provides a new angle to study the decidability of the complexity class MIP*, a longstanding open problem in quantum complexity theory.
