YQI Seminar - Sisi Zhou - Yale/University of Chicago

Event time: 
Thursday, June 25, 2020 - 1:00pm to 2:00pm
Zoom ID: 996-230-4081 See map
Event description: 
Quantum channel estimation with application in covariant quantum error correction
Quantum channel estimation describes the task of estimating unknown parameters in quantum channels. A fundamental goal in the study of quantum channel estimation is to identify the ultimate estimation limit when the unknown channel is applied multiple times. We solve this problem in the asymptotic limit: we show the estimation error scales either O(1/n) or O(1/n^2) w.r.t. the number of quantum channels and obtain a simple criterion determining the scaling. Moreover, in both cases we show the optimal estimation error is computable and also achievable using quantum error correction protocols. Our result not only is a great step towards attaining the ultimate quantum channel estimation limit, but also has wide applications in other fields in quantum information theory. We build a close connection between covariant quantum error correction and quantum channel estimation, and prove powerful lower bounds on the error-correction infidelity for covariant codes (quantum codes whose logical Hamiltonian evolution could be realized by physical ones) under general noise channels.