Fundamental Bounds of Wavefront Shaping of Spatially Entangled Photons

TL;DR

This paper explores the fundamental limits of wavefront shaping for spatially entangled photons in scattering media, revealing quantum-specific enhancement behaviors and optimal strategies for quantum imaging and communication.

Contribution

It provides a theoretical and numerical analysis of how wavefront shaping affects entangled photons, highlighting differences from classical light and identifying optimal configurations.

Findings

Shaping one photon yields classical enhancement ~ (π/4)N.

Shaping both photons before medium reduces enhancement to (~π/4)^2 N.

Symmetric detection schemes can restore perfect correlations with enhancement ~ N.

Abstract

Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations through thick scattering media. We analyze configurations where a spatial light modulator shapes one or both photons, either before or after the medium, and show that the optimal enhancement differs fundamentally from classical expectations. For a system with $N$ modes, we show that shaping one photon yields the classical enhancement $\eta \approx (\pi/4)N$, while shaping both photons before the medium reduces it to $\eta \approx (\pi/4)^2N$. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with $\eta \approx N$, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to $\eta \approx 4.6N$. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.