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

TL;DR

This paper proposes a weak measurement-based scheme for estimating Gaussian states in one-dimensional quantum systems, demonstrating potential advantages over traditional projective measurement methods through state recycling.

Contribution

It introduces a novel weak measurement approach for Gaussian state estimation that can outperform projective methods under specific conditions.

Findings

Weak measurements allow state recycling and improved estimation accuracy.

The scheme outperforms projective measurements in certain regimes.

Recycling of quantum states enhances measurement efficiency.

Abstract

We present a scheme to estimate Gaussian states of one-dimensional continuous variable systems, based on weak (unsharp) quantum measurements. The estimation of a Gaussian state requires us to find position ($q$), momentum ($p$) and their second order moments. We measure $q$ weakly and follow it up with a projective measurement of $p$ on half of the ensemble, and on the other half we measure $p$ weakly followed by a projective measurement of $q$. In each case we use the state twice before discarding it. We compare our results with projective measurements and demonstrate that under certain conditions such weak measurement-based estimation schemes, where recycling of the states is possible, can outperform projective measurement-based state estimation schemes.