Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels

• URL: http://arxiv.org/abs/2301.08402v1
• Date: Fri, 20 Jan 2023 02:34:31 GMT
• Title: Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels
• Authors: Li Gao, Marius Junge, Nicholas LaRacuente
• Abstract summary: We prove an entropic uncertainty relation for two quantum channels. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy.
• Score: 17.153903773911036
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy. As a special case, it gives an improved data processing inequality.

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