Experimental investigation of the role of spatial correlations in optical integration with heralded single photons

TL;DR

The work addresses how spatial correlations in SPDC-produced photon pairs affect optical integration tasks implemented with heralded single photons. It combines a phase-only spatial light modulator with polarization-assisted phase-to-amplitude conversion to perform binary-function integration and draws a conceptual parallel to the DQC1 model, enabling trace-based readout with minimal entanglement. By comparing COR (correlated) and UNC (uncorrelated) SPDC configurations, the authors show that UNC excels at capturing global image features while COR more effectively probes local details, highlighting how spatial correlations shape information processing outcomes. The results illuminate a pathway for quantum-enhanced information processing using photonic systems in regimes where entanglement is not necessarily large, with implications for scalable quantum-inspired optical computing.

Abstract

In this work, we demonstrate optical integration using heralded single photons and explore the influence of spatial correlations between photons on this process. Specifically, we experimentally harness the transverse spatial degrees of freedom of light within an optical processing framework based on heralded single photons. The integration is performed over binary phase patterns encoded via a phase-only spatial light modulator, with polarization serving as an auxiliary degree of freedom. Our findings reveal a distinct contrast in how spatial correlations affect image analysis: spatially uncorrelated photons are more effective at capturing the global features of an image encoded in the modulator, whereas spatially correlated photons exhibit enhanced sensitivity to local image details. Importantly, the optical integration scheme presented here bears a strong conceptual and operational resemblance to the DQC1 (Deterministic Quantum Computation with One Qubit) model. This connection underscores the potential of our approach for quantum-enhanced information processing, even in regimes where entanglement is minimal or absent.

Figures (5)

• Figure 1: Experimental setup for optical processing with single photons: A laser of 405 nm in CW regime pumps a type-II nonlinear crystal. The 810 nm SPDC photons are selected using a frequency filter. The signal photon passes through a phase-to-amplitude modulation system composed of a sequence of optical elements; along this path, it experiences both a Fourier lens and an imaging system, and is detected at $D_1$. The idler photon passes through an imaging system followed by another system that can be configured either as a Fourier lens or as an imaging setup, and is detected at $D_2$.
• Figure 2: Quantum circuit diagram for Deterministic Quantum Computation with one qubit. The Hadamard gate $H$ acts on qubit $\ket{0}$ producing the state $\ket{+}=\frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$, while the controlled operation $U$ acts on the system represented by density matrix $\rho_t$.
• Figure 3: Binary maps prepared in the SLM mask. White cells are groups of pixels of the SLM modulating with phase $\phi = 0$. Black cells are groups of pixels of the SLM modulating with phase $\phi = \pi$.
• Figure 4: Percentage coincidence counting rate $C_+$, with error bars due to poissonian statistics, as a function of $N$, where $N$ is the dimension of the modulated square matrix $N \times N$ on the mask generated by the SLM (some examples are illustrated in Fig. \ref{['pannel']}). Each set of measurements was taken with different proportions of white and black blocks: a) 50%/50%, b) 70%/30%, and c) 90%/10%.
• Figure 5: Coincidence visibility as a function of $D_1$ displacement for three measurement sets. The UNC cases A and B are measured by initially centering detector $D_1$ (imaging plane) at exemplified points A and B of the modulated mask shown in b).