Abstract
Negativity is an entanglement monotone frequently used to quantify entanglement in bipartite states. Because negativity is a nonanalytic function of a density matrix, existing methods used in the physics literature are insufficient to compute its derivatives. To this end 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. The result is an easy-to-implement expansion that can be carried out to all orders. On the way we provide convenient representations of the partial transposition map appearing in the definition of negativity. 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.
- Received 21 September 2018
- Corrected 25 April 2019
DOI:https://doi.org/10.1103/PhysRevA.99.012322
©2019 American Physical Society
Physics Subject Headings (PhySH)
Corrections
25 April 2019
Correction: A misrepresentation of Eq. (D2) introduced during the production cycle has been fixed.