Quantifying Measurement-Induced Disturbance to Distinguish Correlations as Classical or Quantum

In contrast to the conventional entanglement-separability paradigm in quantum information theory, we embark on a different path by introducing a classical dichotomy. We aim to quantify a measurement’s disturbance by minimizing the difference between input and post-measurement states to distinguish either classical or quantum correlations. Theoretically, we apply a complex-valued gradient flow over Stiefel manifolds for minimization. Our focus extends beyond the practical application to encompass the well-known Łojasiewicz gradient inequality. This inequality is a fundamental tool that guarantees the global convergence of the flow from any initial starting point to the optimal solution. Numerically, we validate the effectiveness and robustness of our proposed method by performing a series of experiments in different scenarios. Experimental results suggest the capability of our approach to accurately and reliably characterize correlations as classical or quantum.