⚛️ quantum physics

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

This paper experimentally demonstrates that classical light, utilizing polarization and transverse modes, can reproduce the statistics of the simplest nonclassicality scenario and violate noise-robust inequalities, thereby challenging preparation noncontextuality and bounded ontological distinctness while remaining relevant for semi-device-independent quantum applications.

Original authors: João M. M. Gama, Guilherme T. C. Cruz, Massy Khoshbin, Lorenzo Catani, José A. O. Huguenin, Wagner F. Balthazar

Published 2026-01-26

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CC BY 4.0

Original authors: João M. M. Gama, Guilherme T. C. Cruz, Massy Khoshbin, Lorenzo Catani, José A. O. Huguenin, Wagner F. Balthazar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Can "Fake" Quantum Magic Look Real?

Imagine you are a magician. You have a special deck of cards that, when shuffled and dealt in a specific way, produces a pattern that seems impossible for a normal deck of cards to do. This pattern proves your deck is "special" (or in physics terms, "nonclassical").

Usually, to prove a deck is special, you need to use actual quantum particles (like single photons), which are tiny, fragile, and hard to control.

This paper asks a different question: Can we use a giant, bright, ordinary laser beam (classical light) to mimic the behavior of those tiny quantum particles? If we can make the big laser beam act exactly like the tiny quantum particles, does that mean the "magic" isn't actually magic, or does it mean the rules of the game are deeper than we thought?

The answer the researchers found is: Yes, we can mimic the magic perfectly using ordinary light.

The Setup: The "Simplest" Game

The scientists decided to play the "simplest" possible game where this kind of magic usually happens.

The Players: They prepared four different states of light (like four different ways to hold a card).
The Judges: They used two different ways to measure the light (like two different ways to look at the card).

In the "perfect" quantum world, these four states and two measurements create a specific statistical pattern that classical physics says is impossible. It's like rolling two dice and getting a sum of 15 every time—it shouldn't happen, but if it does, something is weird.

The Experiment: Two Different "Costumes"

To test this, the team used a bright laser and dressed it up in two different "costumes" (degrees of freedom) to see if the magic still worked:

The Polarization Costume: They used the direction the light waves wiggle (up/down or left/right). This is like spinning a coin on a table.
The Shape Costume: They used the shape of the light beam (specifically, a pattern called Hermite-Gaussian modes). This is like taking a flashlight beam and squishing it into a specific flower shape or a donut shape.

They built two different optical setups (using mirrors, lenses, and prisms) to create these four states and measure them.

The "Noise" Problem: The Foggy Window

In the real world, nothing is perfect. There is always "noise" (like dust on a lens or a shaky hand). In quantum experiments, noise usually kills the magic. If you add too much noise, the impossible pattern disappears, and the results look boring and classical again.

The researchers added a special "fog machine" to their experiment. They created a setup that intentionally mixed their perfect light with random noise (simulating a "depolarizing channel"). They wanted to see: How much fog can we add before the magic stops working?

The Results: The Magic Holds Up

Here is what they found:

The Mimicry Worked: Even though they used a bright, classical laser (not single quantum particles), the statistics they measured were identical to what quantum theory predicts for the "simplest scenario."
Breaking the Rules: They tested three different mathematical "rules" (inequalities) that classical physics says should never be broken. Their results broke all three rules.
- Analogy: Imagine a rule that says "You can't have a square circle." Their experiment showed a "square circle" appearing on the screen, proving that the classical light was behaving in a way that defies standard classical logic.
The Noise Limit: They found that as long as the "fog" (noise) was kept below a certain low level (about 0.7% to 2% depending on the test), the magic remained visible. Once the fog got too thick, the pattern faded away.

Why Does This Matter? (According to the Paper)

The paper claims two main things:

Classical Light Can Fool You: You don't need expensive, fragile single-photon sources to see these "nonclassical" signatures. You can use a standard laser and clever optics to reproduce the exact same statistics. This suggests that the "weirdness" of quantum mechanics might be more about the information and the setup than the specific particle being used.
First Time for a Specific Test: This is the first time anyone has experimentally tested a specific concept called Bounded Ontological Distinctness (BODP).
- Simple explanation: This concept asks: "If two things look different to us, are they really different underneath?" The experiment showed that even with classical light, the answer is "No, they aren't distinct in the way classical physics expects."

The Bottom Line

The researchers successfully built a machine using ordinary laser light that acts like a quantum computer for a very specific, simple task. They proved that you can create "quantum-like" behavior with "classical" tools, provided you are careful enough to avoid too much noise.

They didn't build a new phone or a medical scanner. Instead, they built a proof-of-concept showing that the boundary between "classical" and "quantum" is blurrier than we thought, and that the "magic" of quantum statistics can be emulated in a lab using bright, everyday light.

Technical Summary: Experimental Investigation of Nonclassicality in the Simplest Scenario via Degrees of Freedom of Light

Problem Statement
The paper addresses the experimental verification of nonclassicality in the "simplest scenario," defined as a prepare-and-measure protocol involving four preparations and two binary-outcome measurements that form a tomographically complete set. While theoretical frameworks exist to witness nonclassicality through preparation contextuality and violations of bounded ontological distinctness for preparations (BODP), experimental tests have historically relied on single-photon sources. Furthermore, realistic experiments suffer from noise and imperfect operational equivalences, which can obscure nonclassical signatures. The work aims to experimentally test the noise-robust inequalities derived in Khoshbin et al. [Phys. Rev. A 109, 032212 (2024)] using classical light, thereby emulating the operational statistics of the simplest scenario without requiring genuine quantum resources like single photons.

Methodology
The authors implemented the simplest scenario using two distinct experimental setups exploiting different degrees of freedom of an intense classical laser beam (532 nm):

Polarization: The two-level system was encoded in the horizontal-vertical basis ( $|H\rangle, |V\rangle$ ).
Transverse Modes: The system was encoded using first-order Hermite-Gaussian spatial modes ( $|HG_{01}\rangle, |HG_{10}\rangle$ ).

In both setups, four specific states ( $P_{00}, P_{01}, P_{10}, P_{11}$ ) were prepared to approximate ideal vectors on the Bloch circle. Two tomographically complete measurements (X and Y, corresponding to diagonal/anti-diagonal and circular bases) were performed to reconstruct the operational statistics.

To address experimental noise, the authors modeled a depolarizing channel using an all-optical linear circuit. This setup mixed the prepared state with the completely mixed state by controlling the relative intensities of polarization-path components, effectively shrinking the Bloch vector toward the center.

The experimental data were analyzed against three theoretical approaches for witnessing nonclassicality:

Pusey's approach: Testing a robust noncontextuality inequality ( $S$ ).
Marvian's approach: Quantifying "inaccessible information" ( $C_{min}^{prep}$ ).
BODP approach: Testing for violations of parity preservation (a specific case of BODP), quantified by $D_{min}^{P_+, P_-}$ .

The analysis relied on the assumption that the implemented measurements form a tomographically complete set, allowing the reconstruction of the effective two-dimensional operational description.

Key Results
The experimental results from both the polarization and transverse mode setups were consistent with theoretical predictions:

Noise Thresholds: For the unperturbed experiments, the distance between the noisy prepared states and their ideal counterparts ( $\delta$ ) was found to be $\leq 0.007$ . This is well within the theoretical threshold required to violate all three nonclassicality criteria.
Violation of Inequalities:
- Pusey's Inequality: The observed values for $S(x_{ij}, y_{ij})$ ranged from approximately 0.719 to 0.765, significantly exceeding the noncontextual bound of 0.
- Marvian's Measure: The calculated inaccessible information $C_{min}^{prep}$ was consistently $\geq 0.069$ , violating the noncontextual bound of 0.
- Parity Preservation/BODP: The condition $D_{min}^{P_+, P_-} > 0$ was satisfied, indicating a violation of parity preservation and, consequently, BODP.
Depolarizing Noise: When noise was explicitly modeled via the depolarizing channel, the experiment confirmed the theoretical thresholds derived in [1]. Specifically, violations of all three criteria persisted for $\delta \leq 0.02$ , while Pusey's inequality alone remained violated for $\delta \leq 0.07$ .

Significance and Claims
The paper claims several significant contributions:

Classical Emulation of Quantum Statistics: The work demonstrates that classical optical fields (using polarization and spatial modes) can reproduce the operational statistics of the simplest scenario, which underpins computational advantages in tasks like 2-bit quantum random access codes. This validates the use of classical light for probing generalized contextuality.
First Experimental Investigation of BODP Violation: To the authors' knowledge, this is the first experimental investigation specifically targeting the violation of BODP (via parity preservation) in this scenario.
Robustness to Noise: The experiments confirm that the nonclassicality witnesses proposed in [1] are robust against experimental imperfections and noise, successfully overcoming the idealizations of perfect noiseless measurements and exact operational equivalences that often plague such tests.
Scalability and Platform Independence: By utilizing two distinct degrees of freedom, the work suggests that similar results can be achieved with other degrees of freedom (e.g., path, time, frequency) and that these protocols are applicable to integrated and fiber-based platforms.

The authors conclude that their implementation provides a direct experimental verification of the theoretical framework for nonclassicality in the simplest scenario, confirming that preparation contextuality and BODP violations can be observed even with classical light sources, provided the noise remains below specific thresholds.