Information Gain versus State Disturbance for a Single Qubit

Springer Science and Business Media LLC - 2006
Konrad Banaszek1,2
1Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5, PL-87-100 Toruń, Poland
2Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Tóm tắt

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.

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