Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Ahlsde and Winter (IEEE Trans. Inf. Th. 2002) introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables.  present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan (JCSS 1988)). As a consequence,  derandomize an efficient construction by Alon and Roichman (RSA 1994) of an expanding Cayley graph of logarithmic degree on any (possibly non-abelian) group. This gives an optimal solution to the homomorphism testing problem of Shpilka and Wigderson (STOC 2004).  also apply these pessimistic estimators to the problem of solving semidefinite covering problems, thus giving a deterministic algorithm for the quantum hypergraph cover problem of Ahslde and Winter.
['Avi Wigderson', 'David Xiao']
I am writing a research paper on a idea Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications
[{"from": "human", "value": "I am writing a research paper on a idea Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Ahlsde and Winter (IEEE Trans. Inf. Th. 2002) introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables.  present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan (JCSS 1988)). As a consequence,  derandomize an efficient construction by Alon and Roichman (RSA 1994) of an expanding Cayley graph of logarithmic degree on any (possibly non-abelian) group. This gives an optimal solution to the homomorphism testing problem of Shpilka and Wigderson (STOC 2004).  also apply these pessimistic estimators to the problem of solving semidefinite covering problems, thus giving a deterministic algorithm for the quantum hypergraph cover problem of Ahslde and Winter."}]