Entanglement-enabled image transmission through complex media

Abstract

Scattering in complex media scrambles light, thus obscuring images and limiting applications from astronomy to microscopy. Existing computational and wavefront-shaping methods treat scattering as a linear optical-wave inversion problem that aims to render the medium transparent by inverting the scattering process. As classical approaches, they do not account for the quantum nature of the incident field. Here, we demonstrate a quantum-entanglement-based method that enables selective image transmission through complex media. The medium is effectively turned into a quantum-classical image filter via wavefront shaping - images encoded on an entangled two-photon state are transmitted faithfully, while those carried by classical light remain fully scattered and unreadable. This method exploits a property of quantum entanglement - the preservation of photon correlations across multiple measurement bases - that has no classical counterpart. Therefore, we establish an approach for controlling light in complex media by tailoring solutions to the quantum properties of the input state, with potential applications in secure information transmission by rendering channels opaque to classical signals while preserving the quantum link.

Figures (6)

• Figure 1: Rendering a complex medium transparent to entangled photons while remaining opaque to classical light. Two imaging scenarios through a complex medium are shown. On the left, an object encoded in classical light intensity is scattered, producing a speckle pattern at the output. On the right, the object is encoded in the spatial correlations of entangled photon pairs. Despite propagation through the same medium, the measured correlation image reveals the object as if the medium were transparent. This is achieved by tailoring the optical disorder of the medium for implementing a specific basis transformation that preserves quantum correlations and thus the encoded image. Both intensity and correlation images are from numerical simulations detailed in Methods and Supplementary Section IV.
• Figure 2: Experimental setup.a, A continuous-wave laser at 405nm illuminates an object placed in the object plane of a lens $f_0$. The beam is then focused onto a 0.5mm-thick nonlinear $\beta$-barium borate (BBO) crystal, where type-I spontaneous parametric down conversion (SPDC) generates degenerate spatially entangled photon pairs at 810nm. A long-pass filter (LPF) removes the residual pump beam after the crystal. The photon pairs are Fourier-imaged by another lens $f_1$ onto the input plane, which is conjugate to the object plane. Before the object, a dichroic mirror (DM) combines the paths of a superluminescent diode (SLED) and the pump laser. The lasers are switched on or off depending on whether the system operates under quantum or classical illumination. Two confocal telescopes formed by the lenses $f_2$–$f_5$ link the input plane to the output plane. A spatial light modulator (SLM) and a scattering medium (a layer of Parafilm) are positioned in the Fourier planes of the telescopes. The optical transformation $S'$ linking the input plane to the output plane is tailored by programming phase patterns onto the SLM using either a (b) classical or (c) our non-classical wavefront-shaping approach (see Fig. \ref{['fig:Fig3']} for details). Lenses $f_i$ and $f_c$, along with movable mirrors, represent two separate imaging systems with magnification $1$, mapping the output plane onto a Charge-Coupled Device (CCD) camera and a time-stamping Tpx3Cam, respectively. A bandpass filter at $810\pm5$nm (not shown) is used to suppress stray light on both cameras.
• Figure 3: Experimental results. In the quantum case, correlation images of an entanglement-encoded object (the digit '8') are measured (a) without the scattering medium, (b) after propagation through it, after tailoring the medium via (c) classical and (d) non-classical wavefront shaping. The corresponding intensity images, shown in the insets, reveal no information about the object. In the classical case, intensity images are recorded (e) without the scattering medium, (f) after propagation through it, after tailoring it via (g) classical and (h) non-classical wavefront shaping. The same scattering medium and tailoring function (i.e. the same SLM phase pattern) are used in both quantum and classical configurations. Correlations images required $8$-second acquisitions, while classical intensity images were acquired withing a few tens of milliseconds. Each image is normalized to its maximum value. See Supplementary Section I for more details about the experimental setup.
• Figure 4: Optimization process. The sum of the classical correction mask (Fig. \ref{['fig:Fig2a']}b) and a random $0$/$\pi$ mask (a) constitutes an exact solution of Eq. \ref{['eq3ter']}, while preserving neither the classically encoded image (b) nor the entanglement-encoded image (c). d-f, Correlation images measured experimentally using a maximally entangled two-photon state at the input (guide state) without the scattering medium (d), with the scattering medium and before optimization (e), and after optimization (f). g, Optimization curve, showing the variation of the central value in the correlation image in function of the number of steps. The optimization is performed computationally by simulating the experiment on a computer using experimentally measured transmission matrix and two-photon input state. The optimization converges towards an SLM phase mask, shown in Figure \ref{['fig:Fig2a']}c, that is then used experimentally to tailor the scattering medium. h, Phase difference between the non-classical (Fig. \ref{['fig:Fig2a']}c) and classical masks (Fig. \ref{['fig:Fig2a']}b). i, Statistical distribution of the phase values in the difference pattern.
• Figure 5: Results for different objects and complex media. Experimental (a-c) and simulated (d) correlation images obtained with different objects and no medium. e-h, Correlation images obtained with the complex medium and no tailoring. Complex media includes a random phase mask with controllable disorder displayed on the SLM (e), a 1-cm-thick layer of polydimethylsiloxane (PDMS) positioned in a plane conjugate to the SLM (f) and out of plane (g), and a simulated thick scattering medium (h). i-l, Correlation images obtained after tailoring the medium. Insets at the bottom left of each panel show intensity images measured under photon-pair illumination; bottom right insets show the corresponding intensity images acquired under classical illumination. Each image is normalized to its maximum value. See Methods for more details on the simulations.