The Heisenberg-Robertson uncertainty relation presents a lower bound on the product of variance of two observables, and provides a trade-off relation of measurement errors of these two observables for any given quantum states. Recently multi-observable uncertainty relations relating on that product of variances are proposed. Here we experimentally demonstrate these multi-observable uncertainty relations are valid in a state-dependent manner and the lower bound is tight for multi-observable being incompatible on the state of the system being measured. We find the behaviour of multiple incompatible observables agrees with the predictions of quantum theory.

Date Published: 18 September 2018
PDF: 7 pages
Proc. SPIE 10771, Quantum Communications and Quantum Imaging XVI, 1077110 (18 September 2018); doi: 10.1117/12.2318021

Published in SPIE Proceedings Vol. 10771:
Quantum Communications and Quantum Imaging XVI
Ronald E. Meyers; Yanhua Shih; Keith S. Deacon, Editor(s)