Speaker: Peixue Wu (University of Waterloo)
Title: Reverse-type data processing inequality
Zoom talk, link in event description
Abstract:
In this paper, we explore the data processing inequality in quantum information through contraction and expansion coefficients of quantum channels. The contraction coefficient of a quantum channel, with respect to relative entropy, quantifies the degree to which states become indistinguishable as the channel is applied. In contrast, the expansion coefficient characterizes whether any pair of states remain distinguishable after a single channel application. We demonstrate that many quantum channels lack a non-zero expansion coefficient, suggesting its limitations as a standalone measure of information preservation.
To address this, we propose a comparative approach by introducing a relative expansion coefficient, to assess how one channel expands relative entropy compared to another, enabling us to establish a reverse-type data processing inequality for pairs of channels under specific conditions. We show that this relative expansion coefficient is positive for various quantum channel pairs, including depolarizing, generalized dephasing, and amplitude damping channels, highlighting cases where reverse data processing inequalities hold within restricted settings. Our work offers new mathematical tools for assessing the nuances of quantum information preservation across quantum channels. As an application, we construct a class of less noisy quantum channels which are not degradable.
This is ongoing joint work with Paula Belzig, Li Gao and Graeme Smith.
About the seminar: Weekly seminar hosted by the Quantum Working Group. Topics include quantum information theory and related topics in operator algebra. Contact: Felix Leditzky (leditzky@illinois.edu)