Quantum nondemolition measurement saturates fidelity trade-off

Quantum mechanics sets a bound between the quality of estimation from measurement of a single copy of a d-level system and the degree of disturbance of this system. We show that ideal quantum nondemolition (QND) measurement fed by a properly prepared ancilla saturates this bound. The ratio between the quality of estimation and the degree of disturbance can be continuously controlled by preparation of the ancilla. Further, we show that also nonideal QND measurement achieves this bound if a suitable measurement on the ancilla is performed. Finally, we propose a feasible scheme for such a measurement for optical two-level systems that is based on the controlled-NOT gate.