Optimal Estimation of Complex Squeezing in Phase Space

All optical fields fluctuate in both phase and amplitude due to stochastic indeterminacy, which imposes a fundamental shot noise uncertainty to measurements. Squeezed states surpass this precision limit in one quadrature at the expense of a concomitant increased uncertainty to the complementary quadrature. These states are heavily used in continuous variable quantum information processing [1], quantum metrology [2], and optical quantum computing. Full characterisation of the squeezed states used is required to envisage the progression of these applications.

We apply quantum estimation theory to optimally characterise the squeezing parameter ξ. Previous works have been limited to estimates of its magnitude r. However, a complete understanding also requires knowledge of its direction θ. We derive the fundamental precision bounds for both parameters for general Gaussian states. We find that saturating these bounds through simultaneous measurements are prohibited, even asymptotically. Despite this, we show how correlated intensity measurements saturate the individual precision bounds for complete characterisation of squeezed light sources.

[1] - S. L. Braunstein et. al., Rev. Mod. Phys., 77(2), 2005.
[2] - J. Aasi et. al., Nat. Phot., 7, 2013.