# Matrix Discrepancy from Quantum Communication

@article{Hopkins2021MatrixDF, title={Matrix Discrepancy from Quantum Communication}, author={Samuel B. Hopkins and Prasad Raghavendra and Abhishek Shetty}, journal={ArXiv}, year={2021}, volume={abs/2110.10099} }

We develop a novel connection between discrepancy minimization and (quantum) communication complexity. As an application, we resolve a substantial special case of theMatrix Spencer conjecture. In particular, we show that for every collection of symmetric = × = matrices 1 , . . . , = with ‖ 8 ‖ 6 1 and ‖ 8 ‖ 6 =1/4 there exist signs G ∈ {±1}= such that the maximum eigenvalue of ∑ 86= G8 8 is at most $( √ =). We give a polynomial-time algorithm based on partial coloring and semidefinite…

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## 2 Citations

A New Framework for Matrix Discrepancy: Partial Coloring Bounds via Mirror Descent

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This paper introduces a new robust interior point method analysis for semidefinite programming (SDP) and shows that for the case m = Ω(n), it can solve SDPs in m time, suggesting solving SDP is nearly as fast as solving the linear system with equal number of variables and constraints.

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