Institute of Information Science, Academia Sinica

In this talk, we will discuss how to do quantum state tomography using [@BackSlash]tilde{O}(d/[@BackSlash]eps^2) of copies of "conditional samples" for learning a d-dimensional quantum pure state (with additive [@BackSlash]ell_2-norm error [@BackSlash]eps). If we have a state-preparation unitary available rather than just copies of the state, then this [@BackSlash]eps-dependence can be improved further quadratically. This procedure has improved statistical properties and faster runtime compared to earlier pure-state tomography algorithms. We also generalize this procedure to give a near-optimal time-efficient process-tomography algorithm for reflections around bounded-rank subspaces. In turn, it provides a pure-state tomography algorithm that only requires a reflection about the state rather than a state preparation unitary as input.