Time: 1:00 pm Tuesday, 16th May 2017.
Location: SIT 459
Speaker: Nengkun Yu, University of Technology Sydney
Title: Learning classical information in Quantum system—from Pretty Good Measurement to Pretty Good Tomography
We start with a promise problem of extracting information from a single quantum system whose state is known to be in one of several possible states. In the generic case, it is notoriously difficult to find the optimal measurement (learning algorithm), that is the measurement that provides the most possible information about the system’s state. A simple general prescription for a measurement, pretty good measurement, is provided, which is typically not optimal but appears to be quite good.
In early 1970s, A. Holevo (winner of the Claude E. Shannon Award 2016) initiated the study of the problem of quantum state tomography to obtain complete classical information of the unknown quantum system, when i.i.d. copies of the quantum system is provided. This is the quantum analogue of the problem of estimating a probability distribution given some number of samples. Moreover, it could also be viewed as a special and fundamental problem in quantum property testing, the study of which has recently attracted much attention.
We designed an efficient learning algorithm scheme for this problem by generalised the pretty good measurement into pretty good tomography. The optimality of this algorithm is shown by putting this problem into a quantum communication scenario and employing quantum communication complexity bounds as a tool.