Eur. Phys. J. C (2018) 78: 665
https://doi.org/10.1140/epjc/s10052-018-6096-2

Regular Article - Theoretical Physics

Relativistic motion enhanced quantum estimation of -deformation of spacetime

¹ Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, Hunan, P. R. China
² Department of Physics and Astronomy, Center for Theoretical Physics, Seoul National University, Seoul, 08826, South Korea

^* e-mail: jljing@hunn.edu.cn

Received: 5 March 2018
Accepted: 23 July 2018
Published online: 20 August 2018

Abstract

We probe the -deformation of spacetime using a two-level atom as a detector coupled to a -deformed massless scalar field which is invariant under a -Poincaré algebra and written in commutative spacetime. To address the quantum bound to the estimability of the deformation parameter , we perform measurements on the two-level detector and maximize the value of quantum Fisher information over all possible detector preparations. We prove that the population measurement is the optimal measurement in the estimation of the deformation parameter . In particular, we show that the relativistic motion of the detector affects the precision in the estimation of the parameter , which can effectively improve this precision comparing to that of the static detector case by many orders of magnitude.