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Density matrix reconstruction using a Hong–Ou–Mandel quantum interferometer

Vitaly Sukharenko, R. Dorsinville

Published Mar 11, 2025• 0 citations
Publisher

Abstract

We provide a comprehensive analysis of the reconstruction of the density matrix for entangled photon pairs, utilizing polarization measurements within a Hong-Ou-Mandel (HOM) interference framework. The purpose of this study is to develop a new efficient approach for quantum state characterization, leveraging quantum interference to reduce wave dispersion and utilizing the maximum likelihood method for density matrix reconstruction. The model involves projecting the entangled photons onto a set of sixteen unique polarization states, enabling the observation of detailed quantum interference patterns. We use these patterns to reconstruct the density matrix, revealing the system’s quantum state and degree of entanglement. Our findings demonstrate the effectiveness of this method in accurately characterizing the quantum state of light, while leveraging quantum interference to reduce wave dispersion and improve signal quality and resolution. Our study underscores the effectiveness of this method in accurately characterizing the quantum state of light and highlights the essential role of precise density matrix reconstruction in a Hong-Ou-Mandel interferometer without the use of polarizers. The methodology and results presented lay a strong foundation for further research, with implications for improving measurement accuracy and exploring more complex quantum systems in various quantum information applications. • Density matrix of entangled photon pairs using Hong-Ou-Mandel interference profiles. • Quantum interference and density matrix improve signal quality. • Density matrix is reconstructed using HOM interference and maximum likelihood. • Theoretical study on quantum state reconstruction and its role in quantum information.

DOI
10.1016/j.ijleo.2025.172278

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We provide a comprehensive analysis of the reconstruction of the density matrix for entangled photon pairs, utilizing polarization measurements within a Hong-Ou-Mandel (HOM) interference framework. The purpose of this study is to develop a new efficient approach for quantum state characterization, leveraging quantum interference to reduce wave dispersion and utilizing the maximum likelihood method for density matrix reconstruction. The model involves projecting the entangled photons onto a set of sixteen unique polarization states, enabling the observation of detailed quantum interference patterns. We use these patterns to reconstruct the density matrix, revealing the system’s quantum state and degree of entanglement. Our findings demonstrate the effectiveness of this method in accurately characterizing the quantum state of light, while leveraging quantum interference to reduce wave dispersion and improve signal quality and resolution. Our study underscores the effectiveness of this method in accurately characterizing the quantum state of light and highlights the essential role of precise density matrix reconstruction in a Hong-Ou-Mandel interferometer without the use of polarizers. The methodology and results presented lay a strong foundation for further research, with implications for improving measurement accuracy and exploring more complex quantum systems in various quantum information applications. • Density matrix of entangled photon pairs using Hong-Ou-Mandel interference profiles. • Quantum interference and density matrix improve signal quality. • Density matrix is reconstructed using HOM interference and maximum likelihood. • Theoretical study on quantum state reconstruction and its role in quantum information.
Two-photon interference in a Hong-Ou-Mandel (HOM) interferometer can be used as a quantum sensing mechanism due to the sensitivity of the interference dip to perturbations of the photon indistinguishability. In particular, recent works have generalized this concept to microscopy setups, but the sensitivity to optical path differences constrains its application to samples with thickness variation typically below a few micrometers if tracking changes in the coincidences at a fixed delay. Extending the concept to polarization microscopy and circumventing this limitation, this manuscript explores the use of a narrowband photon pair source with coherence length >1 mm to broaden the HOM dip. Thus, realistic sample-thickness variations introduce negligible temporal distinguishability, and changes in coincidence rate at the dip centre are then dominated by sample-induced polarization effects. To compute the polarization rotation, we develop a statistical model for the interferometer, derive the Fisher information, and establish a maximum-likelihood estimator for the local fast-axis angle. Recording dip and baseline frames at each sample position via raster scanning, the experimental results validate the framework, agreeing with classical polarized-intensity images while demonstrating operation at a maximum-precision regime and insensitiveness to layer thickness. Overall, the approach enclosed provides a quantum-based quantitative imaging of birefringent structures, which can motivate further advantageous applications, including enhanced signal-to-noise ratio and lower damage imaging of photosensitive samples.
Abstract Optical interferometry has been a long-standing setup for characterization of quantum states of light. Both linear and the nonlinear interferences can provide information regarding the light statistics and underlying detail of the light-matter interactions. Here we demonstrate how interferometric detection of nonlinear spectroscopic signals may be used to improve the measurement accuracy of matter susceptibilities. Light-matter interactions change the photon statistics of quantum light, which are encoded in the field correlation functions. Application is made to the Hong-Ou-Mandel two-photon interferometer that reveals entanglement-enhanced resolution that can be achieved with existing optical technology.
Quantum entanglement is a vital resource in quantum information processing. High-dimensional quantum entanglement offers advantages that classical systems cannot surpass, particularly in enhancing channel capacity, improving system noise resilience, and increasing sensitivity to external environments. The construction of multimode entanglement in the spectral domain is well-suited for fiber-optic systems. Here, we present a straightforward scheme for generating multimode frequency-bin entanglement using a semiconductor chip through a simple mode conversion. A general model for Hong–Ou–Mandel (HOM) interference with a multimode frequency-bin entangled state is presented and applied to the experiments. The multimode entangled photons we produced exhibit HOM interference with a high-visibility beating pattern, demonstrating a strong relationship with the mode number, mode spacing, and the profile of the single mode. Building on the Fisher information analysis, we explore the relationship between the features in multimode entangled state interference traces and the precision of interferometric measurements even in the presence of experimental nonidealities. This work may deepen the understanding of multimode frequency-bin entanglement and advance the application of multimode HOM interference in quantum sensing.
Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable to d-dimensional photonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.
We present a projection-free method for mapping two-dimensional polarization distributions using Hong-Ou -Mandel (HOM) interference. Conventional polarization characterization techniques, such as Stokes polarimetry, rely on sequential intensity measurements under multiple polarization projections, making their accuracy and sensitivity susceptible to the extinction ratio, calibration errors, and stability of the polarization analysis optics. Our approach overcomes these limitations by exploiting the sensitivity of two-photon bunching to polarization indistinguishability at a balanced beam splitter. Using a HOM interferometer driven by a high-brightness spontaneous parametric down-conversion photon-pair source at 810 nm, we introduced a birefringent vortex waveplate with spatially varying polarization rotations in one interferometer arm and measured the resulting coincidence counts with a high signal-to-noise ratio, enabling projection-free characterization of the sample-induced polarization transformations. This configuration maps spatially dependent polarization variations directly onto coincidence counts, providing a projection-free reconstruction of the polarization distribution. We demonstrate high-fidelity ($\sim959595\%$) reconstruction of the spatial polarization pattern with an angular resolution of approximately ∼0.4∘\sim0.4^\circ∼0.4∘. The use an estimator that saturates the Cramer-Rao bound, computed from the Fisher information, can improve resolution further at the cost of longer acquisition. The proposed quantum-optical technique offers a simple, scalable, and high-precision framework for characterizing structured polarization fields in birefringent materials.
Hong-Ou-Mandel (HOM) interference [1] is a bunching phenomenon based on the bosonic nature of photons. When two photons that are perfectly indistinguishable from each other are mixed using a half beam splitter (HBS), they always bunch and exhibit the absence of coincidence resulting in a specific interferogram called HOM dip. The important property of the HOM interference is that the decrease in coincidence reflects the degree of indistinguishability of the input photons, i.e., it provides information regarding the probability of overlap of the input photons. Thus, this property should enable the estimation of a target photon in an unknown quantum state using a probe photon in a known state. In this work, we realize the above concept as the quantum state tomography (QST) applicable tod-dimensionald\text{-dimensional}d-dimensionalphotonic qudits, which we call HOM-QST [2]. Interestingly, we observe that HOM-QST is robust against various imperfections and that the probe photon can be replaced by classical light. Furthermore, we confirm this by demonstrating a proof-of-principle experiment using two-dimensional polarization qubits.