🔬 optics

Entanglement-enabled image transmission through complex media

This paper demonstrates a quantum-entanglement-based method that utilizes wavefront shaping to selectively transmit images encoded on entangled photon pairs through complex scattering media while blocking classical light, effectively turning the medium into a quantum-classical image filter.

Original authors: Chloé Vernière, Raphaël Guitter, Baptiste Courme, Hugo Defienne

Published 2026-03-18

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CC BY 4.0

Original authors: Chloé Vernière, Raphaël Guitter, Baptiste Courme, Hugo Defienne

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

Imagine you are trying to send a secret message written on a piece of paper through a thick, foggy window covered in random scratches and smudges.

The Old Way (Classical Light):
If you shine a normal flashlight at the paper, the light hits the scratches, bounces around chaotically, and comes out the other side as a messy, unrecognizable blur. To fix this, scientists have been trying to "undo" the scratches. They use super-computers or special mirrors to calculate exactly how the light bounced and try to reverse the process, effectively making the window look clear again. It works, but it's like trying to un-mix a cake; it's hard, and it treats the light like a simple, predictable wave.

The New Way (Quantum Entanglement):
This paper introduces a magical trick. Instead of using a normal flashlight, the researchers use a special "quantum flashlight" that shoots out pairs of light particles (photons) that are entangled.

Think of entangled photons as telepathic twins. Even if they are separated by miles, if you tickle one, the other laughs instantly. They share a secret connection that normal light doesn't have.

Here is how their new method works, using a few analogies:

1. The "Ghost" vs. The "Rock"

Imagine the complex medium (the foggy, scratched window) is a giant, chaotic maze.

Classical light is like throwing a rock into the maze. It hits a wall, bounces, hits another wall, and eventually comes out in a random direction. You can't tell where it started.
Entangled light is like throwing two ghosts that are holding hands. Even though the maze is chaotic, the connection between the two ghosts is so strong that they can navigate the chaos together. If one ghost gets pushed left, the other instinctively knows to move right to stay in sync.

2. The Magic Filter

The researchers found a way to "tune" the chaotic window. They used a special digital mirror (called a Spatial Light Modulator) to rearrange the scratches on the window.

For Normal Light: They arranged the scratches so that normal light (the rock) gets completely scrambled. The image remains a blur.
For Entangled Light: They arranged the scratches in a very specific, weird pattern that looks like random noise to our eyes, but acts like a perfect highway for the telepathic twins. Because the twins are connected, they can "feel" the path through the chaos and emerge on the other side perfectly organized, revealing the hidden image.

3. The "Secret Handshake"

Why does this work?
Normal light carries information in its brightness (how many photons hit a spot). The chaos destroys this brightness pattern.
Entangled light carries information in the relationship between the twins (where they are relative to each other). The researchers discovered that the chaos of the window destroys the brightness but preserves the relationship if you set up the window just right.

It's like a crowded, noisy party where everyone is shouting (the chaos).

If you try to shout a message, no one hears it.
But if you and your friend have a secret handshake (entanglement), you can find each other in the crowd and pass a note, even though everyone else is just making noise. The chaos doesn't break your secret handshake.

Why is this a big deal?

Security: Imagine you want to send a secret message. You can set up a channel that is completely opaque (invisible) to anyone using normal light (like a spy or a hacker). But if you use this "quantum handshake" method, the message comes through crystal clear. It's a hardware-level lock that only quantum keys can open.
Seeing Through the Unseeable: This could help doctors see through thick tissue or astronomers see through turbulent air, but only if they use quantum light. It turns a "problem" (scattering) into a "feature" (a filter).

In a nutshell:
The researchers didn't try to clean the dirty window. Instead, they figured out how to rearrange the dirt so that it acts like a secret filter. It blocks all normal light, making the world look like static, but it lets through a special "quantum signal" that carries the image perfectly, as if the window wasn't there at all. They turned a chaotic mess into a selective doorway that only quantum entanglement can walk through.

1. Problem Statement

Transmitting optical spatial information (images) through complex, disordered media (e.g., biological tissue, turbulent atmosphere, multimode fibers) is a fundamental challenge in optics. Scattering scrambles light, turning clear images into random speckle patterns.

Current Limitations: Existing methods, such as wavefront shaping and computational imaging, treat scattering as a linear optical inversion problem ( $E_{out} = S E_{in}$ ). These methods aim to make the medium transparent by inverting the scattering matrix $S$ to restore the input field.
The Gap: These classical approaches ignore the quantum nature of the incident field. They assume that if a medium is opaque to classical light, it is opaque to all forms of light. The paper posits that quantum entanglement offers a unique degree of freedom that classical linear wave theory cannot access, potentially allowing for image transmission where classical methods fail or, conversely, allowing for selective filtering.

2. Methodology

The authors propose a method to "tailor" the disorder of a complex medium to act as a quantum-classical image filter. This is achieved by exploiting the bilinear propagation of entangled two-photon states.

A. Theoretical Framework

Classical Propagation: Described by a linear transformation $E_{out} = S E_{in}$ . To restore an image, one must find a phase mask such that $S' \approx I$ (Identity).
Quantum Propagation: For entangled photon pairs, the output two-photon wavefunction $\Psi_{out}$ depends bilinearly on the scattering matrix:
$\Psi_{out} = S \Psi_{in} S^t$
where $S^t$ is the transpose of the scattering matrix.
The Key Insight: The authors demonstrate that there exist non-trivial transformations $S'$ (distinct from the identity) that preserve the spatial correlations of an entangled state (allowing the image to be reconstructed) while scrambling classical intensity information.

B. Experimental Setup

Source: A 405 nm laser pumps a Beta Barium Borate (BBO) crystal to generate degenerate, spatially entangled photon pairs at 810 nm via Spontaneous Parametric Down-Conversion (SPDC).
Encoding: Images (e.g., the digit "8") are encoded into the spatial correlations of the photon pairs (specifically, the sum-coordinate projection of the second-order correlation function, $\Gamma_+$ ).
Medium: The light passes through a complex medium composed of a Spatial Light Modulator (SLM) and a scattering layer (Parafilm, PDMS, or a random phase mask).
Detection:
- Classical: A standard CCD/CMOS camera measures intensity (speckle).
- Quantum: A time-stamping camera (Tpx3Cam) measures photon coincidences to reconstruct the correlation image $\Gamma_+$ .

C. Optimization Strategy

Since the theoretical solutions for $S'$ (derived from the approximation $\sigma_r \to 0$ ) are difficult to implement exactly due to finite crystal thickness and experimental constraints, the authors use a numerical optimization approach:

Guide State: A maximally entangled "guide" state (without an object) is used as a reference.
Objective: The algorithm optimizes the SLM phase pattern to maximize the central peak of the correlation image $\Gamma_+$ at the output.
Process: A partitioning algorithm iteratively adjusts SLM pixels to find a phase mask that restores the correlation peak. This process is performed numerically using a pre-measured transmission matrix, then applied to the physical SLM.

3. Key Contributions

Selective Transparency: The paper demonstrates that a complex medium can be tailored to be transparent to quantum correlations while remaining opaque to classical intensity.
Non-Classical Solutions: The authors identify a class of "non-classical" solutions for the scattering matrix transformation. Unlike classical wavefront shaping (which seeks $S' \approx I$ ), these solutions satisfy $S' \neq I$ but still preserve the entangled state's correlations.
Entanglement as a Filter: The method proves that the preservation of the image relies specifically on quantum entanglement, not just classical correlations. Simulations show that classically correlated (separable) states fail to transmit the image through these non-trivial solutions.
Theoretical Proof of Existence: The authors provide a mathematical proof (Supplementary Section XVII) that for any entangled input state and arbitrary complex medium, non-trivial solutions exist that preserve the state, provided the system dimension (Schmidt rank) is $\ge 2$ .

4. Experimental Results

Image Transmission:
- Without Tailoring: Both classical intensity and quantum correlation images are scrambled into speckle.
- Classical Tailoring ( $S' \approx I$ ): Both classical and quantum images are restored.
- Non-Classical Tailoring (The Novel Solution):
  - Quantum Case: The image encoded in entangled correlations is faithfully reconstructed (high fidelity, SSIM $\approx 0.92$ ).
  - Classical Case: The image encoded in classical intensity remains completely scrambled (low fidelity, SSIM $\approx 0.25$ ).
Robustness: The method was tested with various objects and different scattering media (Parafilm, PDMS, random phase masks, and simulated thick media), consistently showing that the medium acts as a filter for classical light while passing quantum information.
Verification of Entanglement Necessity: Numerical simulations confirmed that if the input state is replaced by a classically correlated (separable) state with the same correlation statistics, the non-classical solution fails to restore the image. This confirms the mechanism relies on genuine quantum entanglement.

5. Significance and Applications

Secure Communication: This approach offers a physical layer of security. A communication channel can be made "opaque" to classical eavesdropping (who would only see speckle) while remaining transparent to a quantum user. This provides hardware-level protection against spoofing or blinding attacks, surpassing standard Quantum Illumination.
New Paradigm for Complex Media: It shifts the perspective of complex media from being merely obstacles to be inverted, to being active, programmable components for quantum technologies.
Imaging in Complex Environments: While currently limited by the memory effect and photon flux, the method suggests a pathway for imaging through biological tissues or turbulent atmospheres using quantum correlations, potentially offering advantages over classical adaptive optics in specific scenarios.
Fundamental Physics: The work highlights a fundamental difference between linear wave propagation (classical) and bilinear propagation (quantum), showing that quantum states possess a richer solution space for controlling light in disordered environments.

In summary, the paper establishes that by tailoring the optical disorder of a medium to specific quantum properties, one can create a filter that selectively transmits entangled information while blocking classical signals, a feat impossible with classical wavefront shaping alone.