Fourier-transform quantum phase estimation with quantum phase noise

Abstract For the fundamental task of estimating a phase on an arbitrary quantum process, a variant of Fourier-based quantum phase estimation is devised, which uses a probing signal of multiple entangled qubits. For simple practical implementation, each probing qubit can be applied and measured separately. When the qubits are optimally entangled, the Heisenberg enhanced scaling of the estimation efficiency is obtained. The phase estimation protocol can be applied equally in the presence of quantum phase noise. This enables us to investigate the impact of a generic quantum phase noise on the performance of the Fourier-based phase estimation. Especially it reveals that the strategy found optimal with no noise, gradually loses its optimality as the noise increases. Also, in contrast to the noise-free situation, with noise the presence of entanglement is no longer uniformly beneficial to estimation; there exists an optimal amount of entanglement to maximize the efficiency and above which it becomes detrimental. The results contribute to better knowledge of quantum noise and entanglement for quantum signal and information processing.