# Experimental observation of information flow in the anti-$\mathcal{PT}$-symmetric system

## TL;DR

This paper demonstrates the first experimental observation of information flow oscillations in an anti-$\mathcal{PT}$-symmetric system using quantum simulation, revealing how information can recover or be lost depending on symmetry breaking.

## Contribution

It introduces a quantum circuit algorithm to simulate anti-$\mathcal{PT}$-symmetric systems and reports the first experimental observation of information flow oscillations in such systems.

## Key findings

- Information flow oscillates in anti-$\mathcal{PT}$-symmetric systems.
- Information recovers when symmetry is broken.
- No information recovery in symmetry-unbroken phase.

## Abstract

The recently theoretical and experimental researches related to $\mathcal{PT}$-symmetric system have attracted unprecedented attention because of various novel features and potentials in extending canonical quantum mechanics. However, as the counterpart of $\mathcal{PT}$-symmetry, there are only a few researches on anti-$\mathcal{PT}$-symmetry. Here, we propose an algorithm for simulating the universal anti-$\mathcal{PT}$-symmetric system with quantum circuit. Utilizing the protocols, an oscillation of information flow is observed for the first time in our Nuclear Magnetic Resonance quantum simulator. We will show that information will recover from the environment completely when the anti-$\mathcal{PT}$-symmetry is broken, whereas no information can be retrieved in the symmetry-unbroken phase. Our work opens the gate for practical quantum simulation and experimental investigation of universal anti-$\mathcal{PT}$-symmetric system in quantum computer.