• Corpus ID: 239024320

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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