Improved error-tradeoff and error-disturbance relations in terms of measurement error components

摘要

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report various error-disturbance tradeoff relations by decomposing the measurement errors and disturbance into two different components, namely, operator bias and fuzziness. Our uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements.We also design a quantum circuit to measure the two components of the error and disturbance.