Quantum state certification

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

Authors

• Costin Badescu
• Ryan O'Donnell
• John Wright 0004

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