# Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics

## TL;DR

This paper demonstrates that a two-level quantum system under PT symmetric, non-Hermitian dynamics can violate the Leggett-Garg inequality beyond the Tsirelson bound, reaching the algebraic maximum during PT symmetry breaking.

## Contribution

It reveals that PT symmetric dynamics enable maximum violation of the Leggett-Garg inequality, surpassing traditional quantum bounds in a two-level system.

## Key findings

- LGI violation exceeds Tsirelson bound under PT symmetry breaking
- Maximum violation approaches the algebraic limit
- PT symmetric dynamics enhance quantum temporal correlations

## Abstract

We investigate the three-term Leggett-Garg inequality (LGI) for a two-level quantum system undergoing parity-time (PT ) symmetric dynamics governed by a non-Hermitian Hamiltonian, when a sequence of dichotomic projective measurements are carried out at different time intervals. In contrast to the case of coherent unitary dynamics, violation of LGI is shown to increase beyond the temporal Tsirelson bound approaching the algebraic maximum in the limit of the spontaneous PT symmetry breaking