Hilbert-Schmidt disturbance due to measurement

Abstract

We define quantum state disturbance in terms of Hilbert-Schmidt (HS) distance, finding according to this definition that measurements and unitary operations drive qubit states along straight lines and circles, respectively, in HS geometry. We establish conditions for additive disturbance; the straigh-line signature of quantum measurement is a direct consequence of this additivity. Also, state disturbance defined by HS distance is contrapuntally related to information gain measured by state discrimination probability. We use these quantifiers of state disturbance and information gain to elaborate the trade-off between the two. Explicitly identified in this trade-off between information gain and state disturbance is the mechanism-the measurement strength-that mediates the trade-off.