High-dimensional quantum entanglement in photons offers notable technological advancements over traditional qubit-based systems, including increased information density and enhanced security. However, such high-dimensional states are vulnerable to disruption by complex disordered media, presenting significant challenges in practical applications. Spatially entangled photons are conventionally generated using a nonlinear crystal via spontaneous parametric downconversion. While the effect of disorder on spatially entangled photons in the near field of the crystal is well understood, the impact of disorder in the far field is more complex. In this work, we present a systematic study of the randomization of two-photon correlations caused by arbitrary phase distortions in the far field by breaking it down into odd and even parity components. First, we theoretically show that the two-photon field is only sensitive to the even-parity part of the phase distortion. In follow-up experiments, we employ a deformable mirror to implement random phase distortions, separating the contributions of odd and even parity phases using Zernike polynomials. The experimental results are in agreement with the theoretical predictions. Subsequently, we perform numerical simulations to show that these results extend to stronger degrees of disorder. Our key finding is that, since two-photon correlations are only affected by the even-parity component of phase modulations, the number of independent adaptive optics elements required for optimizing the correlation can be effectively halved, offering a significant practical advantage in managing disorder in quantum systems.
High-dimensional quantum entanglement in photons offers notable technological advancements over traditional qubit-based systems, including increased information density and enhanced security. However, such high-dimensional states are vulnerable to disruption by complex disordered media, presenting significant challenges in practical applications. Spatially entangled photons are conventionally generated using a nonlinear crystal via spontaneous parametric downconversion. While the effect of disorder on spatially entangled photons in the near field of the crystal is well understood, the impact of disorder in the far field is more complex. In this work, we present a systematic study of the randomization of two-photon correlations caused by arbitrary phase distortions in the far field by breaking it down into odd and even parity components. First, we theoretically show that the two-photon field is only sensitive to the even-parity part of the phase distortion. In follow-up experiments, we employ a deformable mirror to implement random phase distortions, separating the contributions of odd and even parity phases using Zernike polynomials. The experimental results are in agreement with the theoretical predictions. Subsequently, we perform numerical simulations to show that these results extend to stronger degrees of disorder. Our key finding is that, since two-photon correlations are only affected by the even-parity component of phase modulations, the number of independent adaptive optics elements required for optimizing the correlation can be effectively halved, offering a significant practical advantage in managing disorder in quantum systems.
High-dimensional quantum entanglement in photons offers significant advantages in quantum technologies, including enhanced information capacity and improved security in communication protocols [1]. However, when entangled photons propagate through complex media-such as turbulent atmospheres or multimode fibers-their spatial correlations degrade, limiting their practical utility [2]. While the effects of disorder near the nonlinear crystal generating entangled photons are well understood [3], the impact of disorder in the far field remains less explored. We have systematically investigated the impact of arbitrary phase distortions in the far field by decomposing the disorder into even- and odd-parity components [4]. Through theoretical analysis, we have demonstrated that only the even-parity component affects two-photon interference, while the odd-parity component leaves photon correlations unchanged, as shown in Fig. 1. To validate this prediction, we used a deformable mirror to introduce controlled phase distortions and experimentally confirm our findings. Additionally, numerical simulations showed that these results hold even for more complex disorders.
Wavefront shaping is a key technique for mitigating scattering in complex media, enabling advanced imaging and optical communication. Yet existing approaches are inherently local, requiring active correction elements - such as spatial light modulators or deformable mirrors - to lie directly in the optical path of the scattered light, which limits their integration into compact imaging systems. Here, we experimentally demonstrate nonlocal wavefront shaping using spatially entangled photon pairs. By applying a phase correction to a photon that never interacts with the scattering medium, we compensate for the distortions experienced by its entangled partner and restore their initial spatial correlations. Our approach physically decouples the wavefront correction from the scattering medium, paving the way for imaging through complex media in compact and otherwise inaccessible systems.
Spatial entanglement is a key resource in quantum technologies, enabling applications in quantum communication, imaging, and computation. However, propagation through complex media distorts spatial correlation, posing a challenge for practical implementations. We introduce a symmetrized genetic algorithm (sGA) for adaptive wavefront correction of spatially entangled photons, leveraging the insight that only the even-parity component of wavefront distortions affects two-photon correlation. By enforcing symmetry constraints, sGA reduces the optimization parameter space by half, leading to faster convergence and improved enhancement within a finite number of generations compared to standard genetic algorithms. In addition, we establish the dependence of enhancement on the signal-to-noise ratio of the feedback signal, which is controlled by detector integration time. This technique enables correction of entanglement degradation, enhancing quantum imaging, secure quantum communication, and quantum sensing in complex environments.
Spontaneous parametric down-conversion (SPDC) is one of the most important sources of entangled photons in quantum optics and underpins a wide range of applications in quantum communication, quantum imaging, quantum sensing, and photonic quantum information processing. In this nonlinear optical process, a pump photon is converted into a pair of lower-energy photons that exhibit strong correlations in multiple degrees of freedom. While the generation of photon pairs is governed by energy and momentum conservation, the resulting biphoton state possesses a rich spatial structure whose properties are determined by the interplay among the pump field, the nonlinear medium, and subsequent propagation. This thesis investigates the spatial properties of entangled photon pairs generated through SPDC, focusing on the evolution of their correlations in the near field and on the behavior of orbital-angular-momentum (OAM) entangled states under tight focusing conditions. A common theme throughout this work is the examination of physical effects that emerge when the full biphoton wavefunction is retained rather than reduced through the simplifying approximations often employed in theoretical treatments. The principal contribution of this thesis concerns the near-field propagation of SPDC photon pairs. The spatial correlations of SPDC-generated photons are commonly analyzed within the thin-crystal approximation, where the biphoton wavefunction is assumed to factorize into independent functions of the sum and difference coordinates. We demonstrate that birefringence-induced transverse walk-off breaks this factorization and introduces an intrinsic coupling between these coordinates. More importantly, this coupling survives free-space propagation and remains observable even for crystals that nominally satisfy the thin-crystal condition. As a result, the joint spatial correlations develop a characteristic tapering near the crystal image plane that cannot be captured by conventional factorized models. Numerical simulations and experimental measurements are found to be in excellent agreement, revealing a previously overlooked feature of SPDC and providing a more complete description of photon-pair generation and propagation in birefringent nonlinear media. The second part of the thesis explores the propagation of OAM-entangled photon pairs beyond the paraxial regime. While OAM correlations are typically studied under weak-focusing conditions, many emerging quantum technologies require structured quantum states to be manipulated in highly confined optical systems. We show that tight focusing modifies the OAM correlation spectrum, leading to a broadening of the accessible mode distribution. This broadening exhibits distinct transverse and longitudinal characteristics and arises from the emergence of nonparaxial field components absent in conventional scalar descriptions. These results provide new insight into the behavior of structured quantum light in strongly focused optical fields and establish a framework for understanding OAM entanglement beyond the paraxial approximation. Together, the results presented in this thesis reveal previously unexplored aspects of the structure and propagation of entangled photon pairs. By moving beyond widely used approximations, this work uncovers physical effects that influence the generation, evolution, and measurement of spatially entangled states, with implications for quantum imaging, high-dimensional quantum communication, and the broader development of structured-light-based quantum technologies.
This paper explores the novel concept of programmable spatiotemporal entanglement, realized through engineered disordered photonic crystals (DPhCs). We propose a theoretical framework that leverages the unique light-matter interaction within these disordered photonic structures. This interaction is characterized by phenomena such as Anderson localization and can be effectively described using random matrix theory. Our goal is to generate and control highly complex entangled states, addressing limitations of traditional methods. Conventional approaches for entanglement generation often struggle with scalability, robust control, and high-dimensional encoding across both spatial and temporal degrees of freedom simultaneously. By introducing controlled disorder into photonic crystal designs, we aim to harness the rich scattering phenomena to tailor the correlations between entangled photons across their spatiotemporal wavefronts. The proposed methodology involves embedding nonlinear optical elements within these disordered structures to facilitate spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM). In such environments, the localized modes and the modified density of states profoundly influence the properties of the emitted photon pairs. Programmability is envisioned through external control mechanisms, such as adaptive wavefront shaping of the pump light or tunable disorder elements. These mechanisms would allow for dynamic manipulation of entanglement properties like dimensionality, purity, and Schmidt mode distributions. We discuss the potential for robust, high-dimensional quantum states and their implications for advanced quantum communication, quantum imaging, and novel quantum computing architectures. This work lays the groundwork for a new paradigm in quantum state engineering, exploiting complexity to achieve unprecedented control over multiphoton entanglement.
Reliable transmission of quantum optical states through real-world environments is key for quantum communication and imaging. Yet, aberrations and scattering in the propagation path can scramble the transmitted signal and hinder its use. A typical strategy is to employ a classical beacon beam to learn and then correct for the wavefront distortions. However, relying on a separate light source increases the overhead in the experimental apparatus. Moreover, the beacon light must closely match the non-classical state in polarization, wavelength, and even temporal bandwidth, which is highly challenging in practice. Here, we introduce a fast and efficient wavefront correction approach where we use the quantum state itself to correct for optical distortion. Via pump shaping, we control the degree of entanglement in the spatially-entangled two-photon state so that it behaves either as a high-dimensional entangled state or as a classical coherent state. The latter case is used to efficiently measure the transmission matrix of the propagation channel and correct its distortions with a spatial light modulator, thereby enabling the transmission of the high-dimensional entangled state with minimal errors. Our approach paves the way for the practical implementation of quantum imaging and communication protocols based on high-dimensional spatially entangled states.