Critical points of the linear entropy for pure L-qubit states

Abstract

We present a substancially improved version of the method proposed in Sawicki et al (2012, 2014) for finding critical points of the linear entropy for L-qubit system. The new approach is based on the corespondance between momentum maps for abelian and non-abelian groups, as described in Kirwan (1984). The proposed method can be implemented numerically much easier than the previous one.

arXiv comment16 pages, 3 figures

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• Multipartite quantum correlations: symplectic and algebraic geometry approach
• A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
• Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems
• Designing locally maximally entangled quantum states with arbitrary local symmetries
• Poincaré polynomials for Abelian symplectic quotients of pure $r$-qubits via wall-crossings