Quantum state certification

• DOI: 10.1145/3313276.3316344
• Publication Date: 2019-06-20T12:19:08Z
• Authors: Costin Bădescu; Ryan O'Donnell; John Wright
• Keywords: TRACE (psycholinguistics); Constant (computer programming); Quantum tomography

We consider the problem of quantum state certification, where one is given n copies an unknown d-dimensional mixed ρ, and wants to test whether ρ equal some known σ or else є-far from σ. The goal use notably fewer than Ω(d2) needed for full tomography on (i.e., density estimation). give two robust certification algorithms: with respect fidelity using = O(d/є) copies, trace distance O(d/є2) copies. latter algorithm also applies when as well. These copy complexities are optimal up constant factors.