Uncertainty-disturbance relations and applications

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them, proving that uncertainty not only serves as a prerequisite for intrinsic disturbance but also bounds it from above. We formalize this connection via uncertainty-disturbance relations (UDRs) with direct applications in quantum information science. We show that for rank-one projective measurements, these UDRs effectively function as uncertainty relations by bounding the uncertainties of incompatible measurements. They also enable the experimental estimation of key quantum resources—including von Neumann entropy, purity, coherence, and genuine randomness. Our findings thus unify the understanding of uncertainty and disturbance and provide a versatile framework for quantum resource detection.