Uncertainty Relations Between Error and Disturbance in Quantum Measurements

Abstract

Heisenberg originally discussed the trade-off relation between error and disturbance in quantum measurement. In this chapter, we prove several trade-off relations between error and disturbance. As shown in Chap. 7, the error and disturbance in measurement are quantified in terms of Fisher information contents. By expanding relevant operators in terms of the generator ${\hat{\mathbf{{\lambda }}}}$ of the Lie algebra, we calculate the error and disturbance, and prove the trade-off relations.