This paper proposes a new quantum-like method for the binary classification applied to classical datasets. Inspired by the quantum Helstrom measurement, this innovative approach has enabled us to define a new classifier, called Helstrom Quantum Centroid (HQC). This binary classifier (inspired by the concept of distinguishability between quantum states) acts on density matrices—called density patterns—that are the quantum encoding of classical patterns of a dataset. In this paper we compare the performance of HQC with respect to twelve standard (linear and non-linear) classifiers over fourteen different datasets. The experimental results show that HQC outperforms the other classifiers when compared to the Balanced Accuracy and other statistical measures. Finally, we show that the performance of our classifier is positively correlated to the increase in the number of “quantum copies” of a pattern and the resulting tensor product thereof.

Recent advances in Quantum Machine Learning (QML) have provided benefits to several computational processes, drastically reducing the time complexity. Another approach of combining quantum information theory with machine learning—without involving quantum computers—is known as Quantum-inspired Machine Learning (QiML), which exploits the expressive power of the quantum language to increase the accuracy of the process (rather than reducing the time complexity). In this work, we propose a large-scale experiment based on the application of a binary classifier inspired by quantum information theory to the biomedical imaging context in clonogenic assay evaluation to identify the most discriminative feature, allowing us to enhance cell colony segmentation. This innovative approach offers a two-fold result: (1) among the extracted and analyzed image features, homogeneity is shown to be a relevant feature in detecting challenging cell colonies; and (2) the proposed quantum-inspired classifier is a novel and outstanding methodology, compared to conventional machine learning classifiers, for the evaluation of clonogenic assays.

We address the problem of finding the optimal common resource for an arbitrary family of target states in quantum resource theories based on majorization, that is, theories whose conversion law between resources is determined by a majorization relationship, such as it happens with entanglement, coherence or purity. We provide a conclusive answer to this problem by appealing to the completeness property of the majorization lattice. We give a proof of this property that relies heavily on the more geometric construction provided by the Lorenz curves, which allows to explicitly obtain the corresponding infimum and supremum. Our framework includes the case of possibly non-denumerable sets of target states (i.e. targets sets described by continuous parameters). In addition, we show that a notion of approximate majorization, which has recently found application in quantum thermodynamics, is in close relation with the completeness of this lattice. Finally, we provide some examples of optimal common resources within the resource theory of quantum coherence.