Information gain versus state disturbance in quantum theory

Andrew Whitaker

Konrad Banaszek

The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state disturbance and the information gain which satisfy certain invariance conditions. This class includes in particular the Shannon entropy versus the operation fidelity. The central role in the derivation is played by efficient quantum operations, which leave the system in a pure output state for any measurement outcome. It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.

Lev B. Levitin

Christopher A. Fuchs, Asher Peres

When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. \textcopyright{} 1996 The American Physical Society.

K. Kraus

Matteo G A Paris

A novel scheme to realize the whole class of quantum nondemolition (QND) measurements of a field quadrature is suggested. The setup requires linear optical components and squeezers, and allows optimal QNDmeasurements of quadratures, which minimize the information gain versus state disturbance trade-off. 1