We propose a physical implementation of time and spatial parity transformations, as well as Galilean boosts, in a trapped-ion quantum simulator. By embedding the simulated model into an enlarged simulating Hilbert space, these fundamental symmetry operations can be fully realized and measured with ion traps. We illustrate our proposal with analytical and numerical techniques of prototypical examples with state-of-the-art trapped-ion platforms. These results pave the way for the realization of time and spatial parity transformations in other models and quantum platforms.
@article{arxiv.1501.07836,
title = {Time and spatial parity operations with trapped ions},
author = {Xiao-Hang Cheng and Unai Alvarez-Rodriguez and Lucas Lamata and Xi Chen and Enrique Solano},
journal= {arXiv preprint arXiv:1501.07836},
year = {2015}
}