Observation of information flow in the anti-𝒫𝒯-symmetric system with nuclear spins
Jingwei Wen, Guo‐Qing Qin, Chao Zheng, Shijie Wei, Xiangyu Kong, Tao Xin, Gui‐Lu Long
Abstract
Abstract The recently theoretical and experimental researches on $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetric system have attracted unprecedented attention because of the various interesting features and potential applications in extending canonical quantum mechanics. However, as the counterpart of $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetry, there are few experimental researches on the anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetric quantum system because of the challenges in simulating anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetry in experiment. Here, we propose an algorithm for simulating the generalized anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetric system in the quantum circuit model. Utilizing the algorithm, we demonstrated the quantum simulation of anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> system experimentally, and an oscillation of information flow is observed in a nuclear magnetic resonance quantum simulator. The experiment showed that the information could recover from the environment completely when the anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetry is broken, whereas no information can be retrieved in the symmetry-unbroken phase. Our work opens the gate for the practical quantum simulation and experimental investigation of universal anti- $${\mathcal{PT}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>PT</mml:mi> </mml:math> -symmetric system in a quantum computer.