Theoretical investigation of dynamics and concurrence of entangled [Formula: see text] and anti-[Formula: see text] symmetric polarized photons

Non-Hermitian systems with parity-time [Formula: see text] symmetry and anti-parity-time [Formula: see text] symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for [Formula: see text] symmetry and [Formula: see text] -symmetry systems have been proposed and realized. Both two-qubits [Formula: see text] -[Formula: see text] and [Formula: see text] -[Formula: see text] symmetric systems have seen an increase in recent years, especially in the dynamics of quantum entanglement. However, to our knowledge, neither theoretical nor experimental investigations have been conducted for the dynamics of two-qubits entanglement in the [Formula: see text] -[Formula: see text] symmetric system. We investigate the [Formula: see text] -[Formula: see text] dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in [Formula: see text] -[Formula: see text] , [Formula: see text] -[Formula: see text] and [Formula: see text] -[Formula: see text] symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the [Formula: see text] -[Formula: see text] symmetrical system, [Formula: see text] -[Formula: see text] symmetrical system, and [Formula: see text] -[Formula: see text] symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a [Formula: see text] -[Formula: see text] symmetric unbroken regime, the entanglement oscillates with two different oscillation frequencies, and the entanglement is well preserved for a long period of time for the case when non-Hermitian parts of both qubits are taken quite away from the exceptional points.