New bounds on private simultaneous quantum message passing

In the private simultaneous message (PSM) setting, $k$ players obtain inputs $x_i\in\{0,1\}^n$ and then independently send messages to a referee, who should learn $f(x_1,...,x_k)$ but no other information about $(x_1,...,x_k)$. The PSM setting was introduced as a minimal model for secure multiparty computation. In the quantum setting, PSM has been related to non-local quantum computation (NLQC), and has several connections to the complexity of Boolean functions. The communication and correlation