Quantum State Estimation Using Weak Measurements

Abstract

We explore the possibility of using 'weak measurements' without 'weak value' for quantum state estimation. Since for weak measurements the disturbance caused during each measurement is small, we can rescue and recycle the state, unlike for the case of projective measurements. We use this property of weak measurements and design schemes for quantum state estimation for qubits and for Gaussian states. We show, via numerical simulations, that under certain circumstances, our method can outperform the estimation by projective measurements. It turns out that ensemble size plays an important role and the scheme based on recycling works better for small ensembles.

Weak measurement-based state estimation of Gaussian states of one-variable quantum systems

“…an intermediate regime of weakness, which leads to optimal information gain. The idea has been explored recently in the context of a qubit with a small ensemble size [7,8]. Weak measurements coupled with postselection have also been employed in the problem of state estimation where a complete characterization of the postselected quantum statistics [9] or the direct measurement of the quantum wavefunction is used [10][11][12].…”