Perturbative expansion of entanglement negativity using patterned matrix calculus

Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. We develop techniques in the calculus of complex, patterned matrices and use them to conduct a perturbative analysis of negativity in terms of arbitrary variations of the density operator. Our methods are well suited to study the growth and decay of entanglement in a wide range of physical systems, including the generic linear growth of entanglement in many-body systems, and have broad relevance to many functions of quantum states and observables.