Theoretical investigation of dynamics and concurrence of entangled $${{\mathcal {P}}}{{\mathcal {T}}}$$ and anti-$${{\mathcal {P}}}{{\mathcal {T}}}$$ symmetric polarized photons

Abstract

Non-Hermitian systems with parity-time $$\mathcal {(PT)}$$ ( PT ) symmetry and anti-parity-time $$\mathcal {(APT)}$$ ( APT ) symmetry have exceptional points (EPs) resulting from eigenvector co-coalescence with exceptional properties. In the quantum and classical domains, higher-order EPs for $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T symmetry and $$\mathcal {APT}$$ APT -symmetry systems have been proposed and realized. Both two-qubits $$\mathcal {APT}$$ APT -$$\mathcal {APT}$$ APT and $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$${{\mathcal {P}}}{{\mathcal {T}}}$$ P T 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 $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$$\mathcal {APT}$$ APT symmetric system. We investigate the $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$$\mathcal {APT}$$ APT dynamics for the first time. Moreover, we examine the impact of different initial Bell-state conditions on entanglement dynamics in $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$${{\mathcal {P}}}{{\mathcal {T}}}$$ P T , $$\mathcal {APT}$$ APT -$$\mathcal {APT}$$ APT and $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$$\mathcal {APT}$$ APT symmetric systems. Additionally, we conduct a comparative study of entanglement dynamics in the $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$${{\mathcal {P}}}{{\mathcal {T}}}$$ P T symmetrical system, $$\mathcal {APT}$$ APT -$$\mathcal {APT}$$ APT symmetrical system, and $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$$\mathcal {APT}$$ APT symmetrical systems in order to learn more about non-Hermitian quantum systems and their environments. Entangled qubits evolve in a $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -$$\mathcal {APT}$$ APT 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.