Violation of Heisenberg's error-disturbance relation by Stern-Gerlach measurements

Abstract: Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed as another aspect of the principle. However, recent developments of quantum measurement theory made Heisenberg's EDR testable to observe its violations. Here, we study the EDR for Stern-Gerlach measurements. In a previous report [arXiv:1910.07929], it has been pointed out that their EDR is close to the theoretical optimal. The present note reports that even the original Stern-Gerlach experiment in 1922, the available experimental data show, violates Heisenberg's EDR. The results suggest that Heisenberg's EDR is more ubiquitously violated than it has long been supposed.