Title: Primitivity for random quantum channels
Speaker: Jing Bai (Harbin Institute of Technology)
Time: Thursday, September 22, 2022. 14:30-15:30.
Location: B201-2, Mingde Building
Abstract：We have considered the primitive index for random quantum channels, which means the minimal natural number n such that the Choi state/matrix of the n-fold composition of channels is full rank. In the previous work, several upper bounds for the index have been obtained, which can be used to construct the so-called (quantum) Wielandt inequality. We note that the optimal upper bound is still an open problem. In our work, we have shown a generic lower bound for the index when the channels are randomly chosen. Our main method is the graphical Weingarten calculus, introduced by Collins and Nechita. Moreover, our result is closely related to the injectivity of the representation of matrix product states. Perez-Garcia et al. claimed that a similar lower bound for the injectivity could be numerically verified, and our result provides a rigorous proof for their argument.
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