A quantum experiment uncertainty principle: A general 2^nd moment uncertainty relation

Abstract

We present a new Quantum Experiment Uncertainty Relation which relates lower bounds on the fluctuations in an experimental measurement to the inherent fluctuations in the tracked observables. In particular, we extend a previous result the Generalized Heisenberg Uncertainty Relation, to obtain a more general quantum uncertainty relation which is useful for n observables and for measurements at different times. We show that all experiments that 'track' the same system operators, share a common lower uncertainty bound, independent of the technology, or the inventiveness of the experimenter. These results are useful for calculating universal lower bounds in different types of experiments, and examples are given for coherent homodyne detection and gravitational wave detection.