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IET conference proceedings.

Compressive tomography of unstructured high-dimensional photonic entanglement

Suraj Goel, Natalia Herrera Valencia, E. Mackay, Saroch Leedumrongwatthanakun, Will McCutcheon, Mehul Malik

Published Nov 13, 2023• 0 citations
Publisher

Abstract

Entanglement-based quantum networks rely upon the characterisation of shared quantum resources between optical links that can scramble entanglement. Here we overcome the significant limitations of tomographing large, unstructured quantum systems to experimentally reconstruct highdimensional states and certify record entanglement dimensionalities through a commercial multi-mode fibre.

DOI
10.1049/icp.2023.2466

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Entanglement-based quantum networks rely upon the characterisation of shared quantum resources between optical links that can scramble entanglement. Here we overcome the significant limitations of tomographing large, unstructured quantum systems to experimentally reconstruct highdimensional states and certify record entanglement dimensionalities through a commercial multi-mode fibre.
High-dimensional photonic entanglement holds significant promise for advancing quantum communication, computation, and metrology. For example, large-alphabet quantum communication protocols are known to benefit from enhanced noise resilience and information capacity via multi-bit time-bin encoding. Yet, characterizing high-dimensional entangled states is challenging, as full state tomography becomes prohibitively costly and often requires unrealizable measurements. Here, we demonstrate a scan-free method to characterize high-dimensional entanglement in the time-frequency domain. Our reconstruction achieves a record 5.70±0.075.70\pm0.075.70±0.07 ebits and a fidelity of 65.4±0.4%65.4\pm0.4\%65.4±0.4% with the maximally entangled state of local dimension 102110211021, certifying the presence of 668668668-dimensional entanglement. We further prove the attainability of a secure key rate of 15.615.615.6 kB/s in a composable finite-size, entanglement-based protocol, and show that in continuous operation, the setup can quickly approach asymptotic key rates. Using commercial telecom components and state-of-the-art low-jitter single-photon detectors, our scalable architecture offers a practical path towards high-rate, noise-resilient quantum communication testbeds.
Fibre transport of multi-dimensional photonic quantum states promises high information capacity per photon without space restriction. This work experimentally demonstrates transmission of spatial ququarts through multi-core optical fibres and measurement of the entanglement between two fibres with quantum state analyzers, each composed of a spatial light modulator and a single-mode fibre. Quantum state tomography reconstructs the four-dimension entangled state that verifies the nonlocality through concurrences in two-dimensional subspaces, a lower bound of four-dimensional concurrence and a Bell-type CGLMP inequality.
In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.