Quantum state certification
Abstract
We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$dimensional quantum mixed state $\rho$, and one wants to test whether $\rho$ is equal to some known mixed state $\sigma$ or else is $\epsilon$far from $\sigma$. The goal is to use notably fewer copies than the $\Omega(d^2)$ needed for full tomography on $\rho$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/\epsilon)$ copies, and one with respect to trace distance using $n = O(d/\epsilon^2)$ copies. The latter algorithm also applies when $\sigma$ is unknown as well. These copy complexities are optimal up to constant factors.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.06002
 Bibcode:
 2017arXiv170806002B
 Keywords:

 Quantum Physics;
 Computer Science  Data Structures and Algorithms