Experimental investigation of nonclassicality in the simplest scenario via the degrees of freedom of light

TL;DR

The paper addresses how to experimentally test nonclassicality in the simplest prepare-and-measure scenario by implementing four preparations and two tomographically complete measurements with classical light. It uses two degrees of freedom (polarization and first-order Hermite–Gaussian modes) and models noise via a depolarizing channel, examining three witnesses: Pusey’s preparation contextuality, Marvian’s inaccessible information, and violations of bounded ontological distinctness for preparations (BOD$_P$) via parity preservation. The results show positive evidence for all witnesses under small noise (e.g., $\boldsymbol{\delta}<0.007$ for parity preservation; $\boldsymbol{\delta}<0.07$ for Pusey; $\boldsymbol{\delta}<0.02$ for parity under depolarizing noise), with both polarization and transverse modes reproducing the predicted statistics, thereby highlighting the robustness of these nonclassicality signatures and their relevance for semi-device-independent protocols. These findings bridge foundational tests of quantum contextuality with practical implementations, suggesting that classical optical platforms can faithfully emulate the operational statistics underpinning quantum communication primitives such as two-bit parity-oblivious multiplexing and related tasks, while offering avenues for future exploration in larger scenarios and alternative noise models.

Abstract

In this work, we experimentally investigate the classical-light emulation of different notions of nonclassicality in the simplest scenario. We implement this prepare-and-measure scenario involving four preparations and two binary-outcome measurements using two distinct experimental setups that exploit different degrees of freedom of light: polarization and first-order Hermite-Gaussian transverse modes. We additionally model experimental noise through an all-optical setup that reproduces the operational effect of a depolarizing channel. Our experimental results are consistent with the findings of Khoshbin et al. [Phys. Rev. A 109, 032212 (2024)]: under the assumption that the two measurements performed form a tomographically complete set, the observed statistics violate their noise-robust inequalities, indicating inconsistencies with preparation noncontextuality and bounded ontological distinctness for preparations. Although our implementation uses classical light, it reproduces the statistics predicted for the simplest scenario. Since the states and measurements of this scenario underpin computational advantages in tasks such as two-bit quantum random access codes -- among the simplest communication primitives enabling semi-device-independent certification of nonclassicality -- our implementation is directly relevant for such applications.

Figures (8)

• Figure 1: Simplest scenario in the noiseless and noisy cases.
• Figure 2: Violation of parity preservation. The black curve indicates the bound in Eq. \ref{['marvian']} while the blue curve indicates the bound in Eq. \ref{['marvian_depol']}. A sufficient condition for $\mathcal{D}^{\min}_{P_{+},P_{-}} > 0$ is given by $f_1(\delta) > f_2(\delta)$, which holds for $\delta\leq 0.02$.
• Figure 3: Experimental setup for state preparation and measurement using polarization.
• Figure 4: Experimental setup for state preparation and measurement using transverse modes.
• Figure 5: Experimental setup to model noise via a depolarizing channel.