Impact of Nonlinear Euler–Heisenberg Electrodynamic Charge on Wormhole Solutions and Light Deflection With Echo Time in Extended Teleparallel Gravity

ABSTRACT A major difficulty in traversable Wormhole (WH) scenario is the necessity of exotic matter arising from the violation of energy conditions within general relativity. This motivates the investigation of modified gravitational frameworks and quantum corrections that may alter the effective stress energy sector and improve the physical viability of such geometries. In this manuscript, we investigate electrically charged traversable WH configurations in linear teleparallel gravity coupled to Euler–Heisenberg nonlinear electrodynamics. A static and spherically symmetric spacetime with a constant redshift function is adopted to obtain an analytic WH solution in which torsion, electric charge, and nonlinear electromagnetic corrections contribute simultaneously to spacetime structure. The physical motivation of this study is that torsion in teleparallel gravity acts as an additional gravitational source, while the Euler–Heisenberg theory represents one loop quantum electrodynamic corrections relevant in strong electromagnetic fields near compact entities. Their combined effect modifies the effective matter distribution and therefore can influence the amount of exotic matter required to support WH throat. We examine geometrical viability conditions, including throat regularity, flaring‐out behavior, and asymptotic flatness. The energy conditions are analyzed in detail and reveal parameter regimes where violations are redistributed and significantly weakened due to torsional and nonlinear electromagnetic contributions. A generalized TOV equilibrium analysis demonstrates that hydrostatic, anisotropic, and quantum correction forces can collectively balance each other, allowing static configurations without introducing additional ad hoc matter sources. We further investigate photon motion around WH geometry by studying photon sphere, critical impact parameter, deflection angle, and echo time delay. We show that the nonlinear electromagnetic charge and torsion parameters produce characteristic optical signatures, modifying photon ring size, bending angle, and echo structure, thereby providing potentially observable distinctions from standard compact entities. Therefore, novelty of this work lies in presenting a self‐consistent scenario where teleparallel torsion and quantum electrodynamic nonlinearities simultaneously first reduce the exotic matter requirement and second generate observable imprints on light propagation around a horizonless compact configuration.