We compare a trade-off between knowledge and decoherence for the incoherent and coherent partial sequential compatible measurements on single-qubit systems. The individual partial measurement nondestructively monitors basis states of the system by single-qubit meter. For the same decoherence caused by this unbiased measurement, the individual coherent measurement gives more knowledge than the incoherent one. For identical sequential coherent measurements, knowledge accumulated not additively increases more slowly than for the incoherent measurements. The overall knowledge can be accumulated using an adaptive measurement strategy on the meters if the single-qubit coherence of meters is kept. On the other hand, preservation of the mutual qubit coherence between the meters necessary for the collective measurement strategy is not required. A loss of single-qubit coherence degrades the coherent measurements back to the incoherent ones. Since the decoherence caused by the measurement process is a quadratic function of knowledge extracted by the individual measurement, Zeno-like behavior can be observed for repetitive weak compatible measurements. This unconditional universal effect does not depend on any dynamics of the qubit and it is a direct consequence of optimally controlled sequential evolution of quantum information.

• Received 6 May 2010

DOI:https://doi.org/10.1103/PhysRevA.83.032311