We consider the problems of testing and learning quantum k-junta channels, which are n-qubit to n-qubit quantum channels acting non-trivially on at most k out of n qubits and leaving the rest of qubits unchanged. We present the algorithms for testing and learning quantum junta channels. This answers an open problem raised by Chen et al. (2023). In order to settle these problems, we develop a Fourier analysis framework over the space of superoperators and prove several fundamental properties, which extends the Fourier analysis over the space of operators introduced in Montanaro and Osborne (2010).

报告人简介：Penghui Yao is an associate professor in the Department of Computer Science, Nanjing University. He obtained his Ph.D. degree in computer science from the Centre for Quantum Technologies (CQT), National University of Singapore. His research interests are in the areas of communication complexity, computational complexity, Pauli analysis and information theory.