Communication Complexity of Distributed High Dimensional Correlation Testing

We consider a two-party distributed hypothesis testing problem for correlated Gaussian random variables. For d-dimensional vector X and scalar variable Y, where Y are jointly with an unknown correlation ?, parties P 1 xmlns:xlink="http://www.w3.org/1999/xlink">2 observe independent copies of respectively. The seek to test if their observations or not, namely they ||?|| exceeds ? is it 0. To that end, communicate interactively declare the output. show roughly order d/? 2 bits communication sufficient necessary resolving above. Furthermore, we establish lower bound d /? needed estimation implying requires less than estimation. Both our bounds hold arbitrary interactive shared randomness, while only one-way randomness. one-dimensional case, probability one error-types fixed, more refined in dependence on other error-type tight even constant.