### Wednesday, October 25, 2017 - 12:00pm to 1:00pm

### Location:

ASA Conference Room 6115 Gates Hillman Centers### Speaker:

COSTIN BADESCU, Ph.D. Student https://www.cs.cmu.edu/~cbadescu/### 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 ε-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/ε) copies and one with respect to trace distance using n = O(d/ε^{2}) copies. The latter algorithm also applies when σ is unknown as well. These copy complexities are optimal up to constant factors.*Joint work with Ryan O'Donnell and John Wright.*

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