Related papers: Prime decomposition and correlation measure of fin…
Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine variety $X \subset \bC^n$. We describe the components associated to $I$ by means of {\em numerical primary decomposition} (NPD). The method is based on the…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal"…
Being the key resource in quantum physics, the proper quantification of coherence is of utmost importance. Amid complex-looking functionals in quantifying coherence, we set forth a simple and easy-to-evaluate approach: Principal diagonal…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
Hilbert-Schmidt (HS) decompositions are employed for analyzing systems of n-qubits, and a qubit with a qudit. Negative eigenvalues, obtained by partial-transpose (PT) plus local unitary transformations (PTU) for one qubit from the whole…
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction…
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…
A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined…
Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits…
For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable.…