2018/09/30 by Jesse C. Cresswell, Ilan Tzitrin, Aaron Z. Goldberg
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Calculus (dental) #Computer science #Density matrix #Discrete mathematics #Eigenvalues and eigenvectors #Mathematics #Matrix (chemical analysis) #Monotone polygon #Multipartite entanglement #Negativity effect #Observable #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Squashed entanglement #Statistical physics #Transpose #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1103/physreva.99.012322
published as Phys. Rev. A 99, 012322 (2019) · 10 pages, 3 figures; as published in PRA
openalex created_date 2018/09/27 · openalex publication_date 2019/01/14 · arxiv created 2019/01/15 · arxiv updated 2019/01/17 · openalex updated_date 2026/08/05
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.