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An on-demand source of bright entangled photon pairs is desirable for quantum key distribution (QKD) and quantum repeaters. The leading candidate to generate entangled photon pairs is based on spontaneous parametric down-conversion (SPDC) in a non-linear crystal. However, there exists a fundamental trade-off between entanglement fidelity and efficiency in SPDC sources due to multiphoton emission at high brightness, which limits the pair extraction efficiency to 0.1% when operating at near-unity fidelity. Quantum dots in photonic nanostructures can in principle overcome this trade-off; however, the quantum dots that have achieved entanglement fidelities on par with SPDC sources (99%) have poor pair extraction efficiencies of 0.01%. Here, we demonstrate a 65-fold increase in the pair extraction efficiency compared to quantum dots with equivalent peak fidelity from an InAsP quantum dot in a photonic nanowire waveguide. We measure a raw peak concurrence and fidelity of 95.3% $\pm$ 0.5% and 97.5% $\pm$ 0.8%, respectively. Finally, we show that an oscillating two-photon Bell state generated by a semiconductor quantum dot can be utilized to establish a secure key for QKD, alleviating the need to remove the quantum dot energy splitting of the intermediate exciton states in the biexciton-exciton cascade., Comment: 24 pages (7 main body, excluding references plus 14 supplemental information) and 4 main body figures