The role of shared randomness in quantum state certification with unentangled measurements

Yuhan Liu, Jayadev Acharya

Given $n$ copies of an unknown quantum state $\rho \in {\mathbb{C}}^{d\times d}$, quantum state certification is the task of determining whether $\rho ={\rho }_0$ or $\Vert \rho -{\rho }_0{\Vert }_1>\epsilon$, wher…