Poincaré polynomials for Abelian symplectic quotients of pure $r$-qubits via wall-crossings

Abstract

In this paper, we compute a recursive wall-crossing formula for the Poincaré polynomials and Euler characteristics of Abelian symplectic quotients of a complex projective manifold under a special effective action of a torus with non-trivial characters. An analogy can be made with the space of pure states of a composite quantum system containing $r$ quantum bits under action of the maximal torus of Local Unitary operations.

References in corpus (2)

• Critical points of the linear entropy for pure L-qubit states
• On the Symplectic Reduced Space of Three-Qubit Pure States

Cited by in corpus (1)

• Cohomological invariants of Abelian symplectic quotients of pure $r$-qubits