High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

Physical unclonable function labels have emerged as a promising candidate for achieving unbreakable anticounterfeiting. Despite their significant progress, two challenges for developing practical physical unclonable function systems remain, namely 1) fairly few high-dimensional encoded labels with excellent material properties, and 2) existing authentication methods with poor noise tolerance or inapplicability to unseen labels. Herein, we employ the linear polarization modulation of randomly distributed fluorescent nanodiamonds to demonstrate, for the first time, three-dimensional encoding for diamond-based labels. Briefly, our three-dimensional encoding scheme provides digitized images with an encoding capacity of 10⁹⁷⁷¹ and high distinguishability under a short readout time of 7.5 s. The high photostability and inertness of fluorescent nanodiamonds endow our labels with high reproducibility and long-term stability. To address the second challenge, we employ a deep metric learning algorithm to develop an authentication methodology that computes the similarity of deep features of digitized images, exhibiting a better noise tolerance than the classical point-by-point comparison method. Meanwhile, it overcomes the key limitation of existing artificial intelligence-driven classification-based methods, i.e., inapplicability to unseen labels. Considering the high performance of both fluorescent nanodiamonds labels and deep metric learning authentication, our work provides the basis for developing practical physical unclonable function anticounterfeiting systems.