The paper presents a method for high-fidelity remote entanglement of trapped atomic qubits using time-bin photons. The authors achieve an entanglement fidelity of 97% between two remote trapped atomic ions, Alice and Bob, by encoding photonic qubits in the timing of their pulses. This approach removes sensitivity to polarization errors, enables long-distance quantum communication, and is scalable to quantum memories with more than two states. The entanglement is established through a measurement-based error detection process and suppression of atomic recoil errors. The study demonstrates that entanglement fidelities beyond 99.9% are feasible, making it a promising method for modular scaling of quantum computers and long-distance quantum communication. The experimental setup involves laser cooling, state preparation and measurement (SPAM), and coherent rotations of the atomic qubits. The fidelity is characterized by measuring qubit correlations in different bases, and the impact of atomic recoil and polarization drifts on the fidelity is analyzed. The results show that stabilizing the laser power and improving cooling techniques can significantly enhance the fidelity and entanglement rate.The paper presents a method for high-fidelity remote entanglement of trapped atomic qubits using time-bin photons. The authors achieve an entanglement fidelity of 97% between two remote trapped atomic ions, Alice and Bob, by encoding photonic qubits in the timing of their pulses. This approach removes sensitivity to polarization errors, enables long-distance quantum communication, and is scalable to quantum memories with more than two states. The entanglement is established through a measurement-based error detection process and suppression of atomic recoil errors. The study demonstrates that entanglement fidelities beyond 99.9% are feasible, making it a promising method for modular scaling of quantum computers and long-distance quantum communication. The experimental setup involves laser cooling, state preparation and measurement (SPAM), and coherent rotations of the atomic qubits. The fidelity is characterized by measuring qubit correlations in different bases, and the impact of atomic recoil and polarization drifts on the fidelity is analyzed. The results show that stabilizing the laser power and improving cooling techniques can significantly enhance the fidelity and entanglement rate.