Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

TLDR

Heisenberg’s uncertainty principle is rigorously proven for intrinsic uncertainties, but the measurement‑disturbance relationship he originally proposed is not formally proven, though it is widely taught as part of the broader principle. The study experimentally tests a violation of Heisenberg’s measurement‑disturbance relationship using weak measurements before and after a system interacts with a measurement apparatus. The experiment implements Lund and Wiseman’s 2010 proposal to confirm Ozawa’s 2003 revised measurement‑disturbance relationship. The results suggest broad implications for quantum mechanics foundations and practical quantum measurement.

Abstract

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's uncertainty principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.