2021/03/04 by Xie, Wei
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2103.02837
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses O(ε-4ln |P|) copies of an unknown state to distinguish whether the unknown state is contained in or ε-far from a finite set P of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that one can distinguish whether an unknown unitary U is equal to or ε-far from a known or unknown unitary V in fixed dimension with O(ε-2) uses of the unitary, in which the Choi state is used and thus an ancilla system is needed. We give an algorithm that distinguishes the two cases with O(ε-1) uses of the unitary, using much fewer or no ancilla compared with previous results.