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Paper

Quantum channel tomography and estimation by local test

Abstract

We study the estimation of an unknown quantum channel with input dimension , output dimension and Kraus rank at most . We establish a connection between the query complexities in two models: (i) access to , and (ii) access to a random dilation of . Specifically, we show that for parallel (possibly coherent) testers, access to dilations does not help. This is proved by constructing a local tester that uses queries to yet faithfully simulates the tester with queries to a random dilation. As application, we show that: - queries to suffice for channel tomography to within diamond norm error . Moreover, when , we show that the Heisenberg scaling can be achieved, even if is not a unitary channel: - queries to suffice for channel tomography to within diamond norm error , and queries suffice for the case of Choi state trace norm error . - queries to suffice for tomography of the mixed state to within trace norm error .