Existence of a robust optimal control process for efficient measurements in a two-qubit system

The verification of quantum entanglement is essential for quality control in quantum communication. In this work, we propose an efficient protocol to directly verify the two-qubit entanglement of a known target state through a single expectation value measurement. Our method provides exact entanglement quantification using the currencence measure without performing quantum state tomography. We prove the existence of a unitary transformation that drives the initial state of a two-qubit system to a designated final state, where the trace over a chosen observable directly yields the concurrence of the initial state. Furthermore, we implement an optimal control process of that transformation and demonstrate its effectiveness through numerical simulations. We also show that this process is robust to environmental noise. Our approach offers advantages in directly verifying entanglement with low circuit depth, making it suitable for industrial-scale quality control of entanglement generation. Our results, presented here, provide mathematical justification for our earlier computational experiments.