The problem of identifying maximally entangled quantum states of a composite quantum
systems is analyzed. We review some states of multipartite systems distinguished with …

We propose general notions to deal with large scale polynomial optimization problems and
demonstrate their efficiency on a key industrial problem of the 21st century, namely the …

The geometric measure of entanglement for pure states has attracted much attention. On the
other hand, the spectral theory of non-negative tensors (hypermatrices) has been developed …

This paper is concerned with the computation of the principal components for a general
tensor, known as the tensor principal component analysis (PCA) problem. We show that the …

We study tensor analysis problems motivated by the geometric measure of quantum
entanglement. We define the concept of the unitary eigenvalue (U-eigenvalue) of a complex …

We provide methods for computing the geometric measure of entanglement for two families
of pure states with both experimental and theoretical interests: symmetric multiqubit states …

We propose a practical entanglement classification scheme for general multipartite pure
states in arbitrary dimensions under local unitary equivalence by exploiting the high order …

We consider the problem of finding the global optimum of a real-valued complex polynomial
on a compact set defined by real-valued complex polynomial inequalities. It reduces to …

In this paper, we study the sparsity-adapted complex moment-Hermitian sum of squares
(moment-HSOS) hierarchy for complex polynomial optimization problems, where the …

In one study, Hillar and Lim famously demonstrated that “multilinear (tensor) analogues of
many efficiently computable problems in numerical linear algebra are nondeterministic …