Allowed region and optimal measurement for information versus disturbance in quantum measurements

摘要

We present graphs of information versus disturbance for general quantum measurements of completely unknown states. Each piece of information and disturbance is quantified by two measures: (i) the Shannon entropy and estimation fidelity for the information and (ii) the operation fidelity and physical reversibility for the disturbance. These measures are calculated for a single outcome based on the general formulas derived by the present author (Terashima in Phys Rev A 93: 022104, 2016) and are plotted on four types of information-disturbance planes to show their allowed regions. In addition, we discuss the graphs of these metrics averaged over all possible outcomes and the optimal measurements when saturating the upper bounds on the information for a given disturbance. The results considerably broaden the perspective of trade-offs between information and disturbances in quantum measurements.