Related papers: Comment on "Matrix Pencils and Entanglement Classi…

We consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical…

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus…

We propose a generalization of the usual SLOCC and LU classification of entangled pure state fermionic systems based on the Spin group. Our generalization uses the fact that there is a representation of this group acting on the fermionic…

We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of SLOCC classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum…

In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear…

We consider a single copy of a pure four-partite state of qubits and investigate its behaviour under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of…

Initialization of composite quantum systems into highly entangled states is usually a must to allow their use for quantum technologies. However, the presence of unavoidable noise in the preparation stage makes the system state mixed, thus…

Consider a multivariable state space system and associated transfer function G({\lambda}). The aim of this paper is to define and analyze two vector spaces of matrix pencils associated with the matrix G({\lambda}) and show that almost all…

In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et al. obtained a finite yet systematic classification of multi-particle entanglement. It is well known that under SLOCC, pure states of three (four) qubits are…

Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps…

We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge…

The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…

We investigate the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for fixed numbers of qubits. We explicitly exhibit the homomorphism between complex and real groups for two-qubits,…

Entanglement is a central resource in quantum information and quantum technologies, yet its characterization remains challenging due to both theoretical complexity and measurement requirements. Machine learning has emerged as a promising…

Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…

Particle filter (PF) sequential Monte Carlo (SMC) methods are very attractive for the estimation of parameters of time dependent systems where the data is either not all available at once, or the range of time constants is wide enough to…

This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…

We provide polynomial-time reductions between three search problems from three distinct areas: the P-matrix linear complementarity problem (P-LCP), finding the sink of a unique sink orientation (USO), and a variant of the $\alpha$-Ham…

One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more…

We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…