$mathcal{PT}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a Parity-Time ($mathcal{PT}$) symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e., the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett-Garg inequality tests show maximal violation about the EPs.