Publications

@article{Tan2026Direct,

title = {Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests},

author = {Xu Kang Tan and Jesvita Menezes and Sanjan D. Murthy and Adetunmise Charles Dada},

url = {https://arxiv.org/abs/2608.28235},

doi = {10.48550/arXiv.2608.28235},

year  = {2026},

date = {2026-08-28},

journal = {arXiv preprint arXiv:2608.28235},

abstract = {Entangled photons play a crucial role in quantum applications, and determining and characterising their entanglement is vital to using them effectively. High-dimensional entangled states offer richer possibilities, but their additional measurement degrees of freedom make them increasingly demanding to characterise. However, adaptive Bell-test methods based on complex simultaneous perturbation stochastic approximation (CSPSA) have so far focused mainly on qubits. Here we numerically investigate a Bell-inequality-violation-based method for detecting entanglement in unknown quantum states. We extend CSPSA to high-dimensional Bell testing by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality for bipartite qudits. The resulting protocol can detect Bell-nonlocal correlations in unknown entangled states, whether pure or mixed, without first reconstructing their density matrix. Using 100 optimisation iterations in each of 100 independent finite-shot runs per number of dimensions d, we demonstrate certified CGLMP violations throughout d=2-8. For isotropic mixed states tested at a visibility of just 0.05 above the standard-Fourier violation threshold, we likewise observe confidence-certified CGLMP violations throughout the range of d studied. We compare this direct stochastic approach with quantum state tomography, the standard method for characterising an unknown state. In the matched benchmark, CSPSA uses fewer measurement configurations per attempt from d=6, whereas tomography requires fewer detected pairs per certified result through d=8. We also derive the phase dependence of the CGLMP parameter and clarify the features of its landscape that govern the adaptive search. Because the measurement-setting cost of each CSPSA iteration is independent of dimension, the method offers a particularly attractive route to the certification of high-dimensional entanglement.},

keywords = {High-dimensional entanglement, Quantum Entanglement, Quantum Measurements, Quantum optics},

pubstate = {published},

tppubtype = {article}

}

@article{dada2011experimental,

title = {Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities},

author = {Adetunmise Charles Dada and Jonathan Leach and Gerald S Buller and Miles J Padgett and Erika Andersson},

url = {https://doi.org/10.1038/nphys1996},

year  = {2011},

date = {2011-01-01},

journal = {Nature Physics},

volume = {7},

number = {9},

pages = {677\textendash680},

publisher = {Nature Publishing Group},

keywords = {High-dimensional entanglement, Parametric downconversion, Photon orbital angular momentum, Quantum Entanglement, Quantum optics, Sources, SPDC},

pubstate = {published},

tppubtype = {article}

}

@article{dada2011bell,

title = {On bell inequality violations with high-dimensional systems},

author = {Adetunmise Charles Dada and Erika Andersson},

url = {https://doi.org/10.1142/S021974991100843X},

year  = {2011},

date = {2011-01-01},

journal = {International Journal of Quantum Information},

volume = {9},

number = {07n08},

pages = {1807\textendash1823},

publisher = {World Scientific},

keywords = {High-dimensional entanglement, Quantum Entanglement},

pubstate = {published},

tppubtype = {article}

}