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arXiv · 2004.09736

Multiple uncertainty relation for accelerated quantum information

Chen Qian·Ya-Dong Wu·Jia-Wei Ji·Yunlong Xiao·Barry C. Sanders
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Abstract

The uncertainty principle, first introduced by Heisenberg in inertial frames, clearly distinguishes quantum theories from classical mechanics. In non-inertial frames, its information-theoretic expressions, namely entropic uncertainty relations, have been extensively studied through delocalized quantum fields, and localization of the quantum fields were discussed as well. However, infeasibility of measurements applied on a delocalized quantum field due to the finite size of measurement apparatuses is left unexplained. Therefore, physical clarification of a quantum protocol revealing entropic uncertainty relations still needs investigation. Building on advances in quantum field theories and theoretical developments in entropic uncertainty relations, we demonstrate a relativistic protocol of an uncertainty game in the presence of localized fermionic quantum fields inside cavities. Moreover, a novel lower bound for entropic uncertainty relations with multiple quantum memories is given in terms of the Holevo quantity, which implies how acceleration affects uncertainty relations.

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Chen Qian, Ya-Dong Wu, Jia-Wei Ji, Yunlong Xiao, Barry C. Sanders. 2020-04-21. Multiple uncertainty relation for accelerated quantum information. https://doi.org/10.1103/physrevd.102.096009

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