Optimal sensing of photon addition and subtraction on nonclassical light

TL;DR

This paper shows that the Wasserstein distance $W_{1}$ effectively measures changes in nonclassical states of light caused by photon addition or subtraction, capturing interference effects and state modifications in optical tomograms.

Contribution

It introduces the use of Wasserstein distance $W_{1}$ as a universal and sensitive measure for detecting photon-induced changes in nonclassical light states, applicable to various quantum states.

Findings

$W_{1}$ accurately reflects photon addition/subtraction effects.

Photon changes shift intensity regions in the optical tomogram.

$W_{1}$ depends on squeezing parameters and quadrature choice.

Abstract

We demonstrate that the Wasserstein distance $W_{1}$ corresponding to optical tomograms of nonclassical states faithfully captures changes that arise due to photon addition to, or subtraction from, these states. $W_{1}$ is a true measure of distance in the quantum state space, and is sensitive to the underlying interference structures that arise in the tomogram after changes in the photon number. Our procedure is universally applicable to the cat and squeezed states, the former displaying the characteristic negativity in its Wigner function, while the latter does not do so. We explicate this in the case of the squeezed vacuum and even coherent states and show that photon addition (or subtraction) is mirrored in the shift in the intensity of specific regions in the tomogram. Further, we examine the dependence of $W_{1}$ on the squeezing parameter, and its sensitivity to different quadratures.