Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation

TL;DR

This paper investigates the fundamental trade-off between information gain and disturbance when estimating a quantum unitary transformation, providing a complete solution and optimal network construction for the problem.

Contribution

It introduces a comprehensive analysis of the information-disturbance trade-off specific to quantum unitary estimation and derives the optimal measurement strategy and network.

Findings

Derived the optimal trade-off curve for quantum unitary estimation.

Provided an explicit construction of the optimal quantum network.

Solved the problem for unitaries distributed according to the invariant measure.

Abstract

We address the problem of the information-disturbance trade-off associated to the estimation of a quantum transformation, and show how the extraction of information about the a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal trade-off curve and presenting an explicit construction of the optimal quantum network.