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Entanglement is a key resource for quantum information processing. A widely used tool for detecting entanglement is entanglement witness, where the measurement of the witness operator is guaranteed to be positive for all separable states…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
We address the problem of optimising entanglement witnesses when a limited fixed set of local measurements can be performed on a bipartite system, thus providing a procedure, feasible also for experiments, to detect entangled states using…
It is shown that, every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide…
Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…
Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are…
In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…
Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features, especially for…
We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using…
Over the past two decades, support vector machine (SVM) has become a popular supervised machine learning model, and plenty of distinct algorithms are designed separately based on different KKT conditions of the SVM model for…
We study entanglement witness and present a construction of entanglement witnesses in terms of the symmetric informationally complete measurements (SIC-POVM). The capability of our witness is shown by some examples and it can be found this…
Detection of entangled states is essential in both fundamental and applied quantum physics. However, this task proves to be challenging especially for general quantum states. One can execute full state tomography but this method is time…
Support vector machine (SVM) has achieved many successes in machine learning, especially for a small sample problem. As a famous extension of the traditional SVM, the $\nu$ support vector machine ($\nu$-SVM) has shown outstanding…
In this paper we promote the use of Support Vector Machines (SVM) as a machine learning tool for searches in high-energy physics. As an example for a new- physics search we discuss the popular case of Supersymmetry at the Large Hadron…
The support vector machine (SVM) and deep learning (e.g., convolutional neural networks (CNNs)) are the two most famous algorithms in small and big data, respectively. Nonetheless, smaller datasets may be very important, costly, and not…
From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…