2014/09/30 by Anna Vershynina · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Convex analysis #Convex combination #Convex optimization #Convex set #Gaussian #Geometry #Mathematics #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Regular polygon #State (computer science) #Stochastic Gradient Optimization Techniques #msc:68Q12 #msc:81P45 #msc:81P50 #msc:81P68 #quant-ph
paper · pdf · doi:10.1103/physreva.90.062329
published as Phys. Rev. A 90, 062329 (2014)
arxiv created 2014/12/01 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a criterion that determines whether a fermionic state is a convex combination of pure Gaussian states. This criterion is complete and characterizes the set of convex-Gaussian states from the inside. If a state passes a program it is a convex-Gaussian state and any convex-Gaussian state can be approximated with arbitrary precision by states passing the criterion. The criterion is presented in the form of a sequence of solvable semidefinite programs. It is also complementary to the one developed by de Melo, \ifmmode \acuteC\else 'C\fiwikli\ifmmode \acuten\else 'n\fiski, and Terhal, which aims at characterizing the set of convex-Gaussian states from the outside. Here we present an explicit proof that criterion by de Melo et al. is complete by estimating a distance between an n-extendible state, a state that passes the criterion, to the set of convex-Gaussian states.