The gate-voltage-dependent differential conductance in quantum point contacts, shaped by entangled-state tunneling, is demonstrated through the gate-voltage-induced displacement of a localized spin. This displacement leads to left-right asymmetric Kondo coupling at low gate voltages, transitioning to symmetric Kondo coupling at higher voltages. To analyze this behavior, we employ the Green's function technique in Liouville space, which allows for the systematic construction of basis vectors represented by operators. The entanglement between left and right dynamics gives rise to an additional coherent side peak, which plays a crucial role in reproducing the observed differential conductance line shape. By determining model parameters phenomenologically, we successfully replicate the experimentally observed gate-voltage-dependent conductance features.
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