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arXiv:2003.04391 · Optics Letters

Efficient compressive and Bayesian characterization of biphoton frequency spectra

Emma M. Simmerman, H.-H. Lu, Andrew M. Weiner, J. M. Lukens

Published Apr 21, 2020• 12 citations
arXivHTMLPDF

Abstract

Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantification of uncertainty. These efficient methods of biphoton characterization should advance our ability to use the high degree of parallelism and complexity afforded by frequency-bin encoding.

DOI
10.1364/ol.392694

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Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantification of uncertainty. These efficient methods of biphoton characterization should advance our ability to use the high degree of parallelism and complexity afforded by frequency-bin encoding.
Frequency-bin encoding provides a scalable platform for photonic quantum information processing by enabling high-dimensional qudit states compatible with the telecommunications infrastructure. However, characterizing these systems remains challenging, as conventional quantum state tomography requires measurement resources that increase rapidly with dimensionality, compounded by the difficulty of implementing controllable measurements across many frequency modes at once. Here, we address these challenges and demonstrate threshold quantum state tomography of entangled frequency-bin qudits using adaptive measurements that exploit the sparsity of highly entangled biphoton frequency combs. Combined with Bayesian inference, we experimentally demonstrate full state estimation of biphoton frequency combs with Hilbert space dimensions up to d2=100d^2=100d2=100---a 56% increase over the previous record---all while performing a mere 1.9% of the measurements required by conventional tomographically complete approaches. This work confirms the promise of measurement-aware approaches for characterizing high-dimensional photonic quantum systems, unlocking new tools for full tomography that are hardware-efficient, state-aware, and free from a priori assumptions about state structure.
Compressive sensing utilizes sparsity to realize efficient image reconstruction. It is a valuable processing technique when cost, power, technology or computational overhead are limited or high. In the quantum domain technology usually limits efficient acquisition of weak or fragile signals. I will discuss the basics of information theory, compression, and compressive sensing. I will then discuss our recent work in compressive sensing. The topics of discussion include low-flux laser Radar, photonic phase transitions, high resolution biphoton ghost imaging, Ghost object tracking, 3D object tracking and high dimensional entanglement characterization. I will touch lightly on our current work of rapid wavefunction reconstruction and wavefront sensing. As an example (shown below), we were able efficiently and rapidly reconstruct high dimensional joint probability functions of biphotons in momentum and position. With conventional raster scanning this process would take approximately a year, but using double-pixel compressive sensing, the pictures were acquired in a few hours with modest flux.
Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si3N4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.
This thesis explores how spectral-temporal structure in quantum optical fields can be used for state reconstruction and metrology. We utilize continuous-frequency modes as a framework for describing quantum correlations and parameter encoding. In the first part, we develop compressive stimulated emission tomography (CSET) to reconstruct the joint spectral amplitude (JSA) of biphoton states generated through spontaneous parametric downconversion. We perform stimulated emission measurements together with compressive sensing methods to recover high-dimensional quantum states from a reduced dataset. Spectral phase is incorporated using frequency-resolved optical gating, which experimentally characterizes the spectral amplitude and phase of the seed pulses and allows them to be directly integrated into the reconstruction model. The resulting inverse problem is formulated as a constrained convex optimization task, enabling recovery of the full complex JSA. Informational completeness certification is used to evaluate the adequacy of the measurement set, and the method is validated using both simulated and experimental data, showing accurate and robust reconstruction under noise and limited sampling. In the second part, we study quantum metrology in structured optical fields, focusing on frequency-comb ranging in dispersive media. We use quantum Fisher information to relate parameter sensitivity to spectral mode geometry. Our results suggest that bandwidth and modal structure play a significant role in determining precision, while squeezing offers limited benefit under loss. Overall, spectral-temporal modes appear to play a central role in both quantum state reconstruction and metrology tasks considered in this work.