Rank-dependant factorization of entanglement evolution

Nonnegative Rank Factorization via Rank Reduction

Abstract. Any given nonnegative matrix A ∈ R can be expressed as the product A = UV for some nonnegative matrices U ∈ R and V ∈ R with k ≤ min{m, n}. The smallest k that makes this factorization possible is called the nonnegative rank of A. Computing the exact nonnegative rank and the corresponding factorization are known to be NP-hard. Even if the nonnegative rank is known a priori, no simple ...

Strong Rank Revealing Cholesky Factorization

STRONG RANK REVEALING CHOLESKY FACTORIZATION M. GU AND L. MIRANIAN y Abstract. For any symmetric positive definite n nmatrixAwe introduce a definition of strong rank revealing Cholesky (RRCh) factorization similar to the notion of strong rank revealing QR factorization developed in the joint work of Gu and Eisenstat. There are certain key properties attached to strong RRCh factorization, the im...

Factorization of rank two theta functions

A Factorization Law for Entanglement Decay

Thomas Konrad, ∗ Fernando de Melo, † Markus Tiersch, ‡ Christian Kasztelan, § Adriano Aragão, 2, ¶ and Andreas Buchleitner ∗∗ Quantum Research Group, School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str.38, D-01187 Dresden, Germany Institut für Theoretische Physik C, RWTH Aachen, D-52056 Aa...

Factorization and Entanglement in Quantum Systems

We discuss the question of entanglement versus separability of pure quantum states in direct product Hilbert spaces, and the relevance of this issue to physics. Different types of separability may be possible, depending on the particular factorization of the Hilbert space. A given orthonormal basis set for a Hilbert space is defined to be of type (p,q) if p elements of the basis are entangled a...