Optimal quantum measurements for additive information and disturbance measures

Abstract

Additive measures for information and disturbance in quantum measurements of a system are defined from well-known multiplicative measures such as estimation and operation fidelities using a logarithm. This is motivated by the fact that information and disturbance are naturally assumed to be additive while performing independent measurements on separable systems. Although the additivity makes no remarkable difference when information and disturbance are separately considered, it can change measurements that only introduce minimal disturbance relative to the amount of information. Such optimal measurements are shown for additive information and disturbance measures with a tradeoff relationship.