Constructing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-qubit entanglement monotones from antilinear operators

TLDR

For qubits, the comb operators are inherently invariant under SL(2,ℂ). The study introduces a method to construct entanglement measures for pure multipartite qubit states and applies it to classify inequivalent types of genuine four‑qubit entanglement. The method employs an antilinear operator, termed a comb, to generate entanglement measures for multipartite qubit states. The comb‑derived filters are entanglement monotones, and the authors provide alternative formulas for concurrence and the three‑tangle as expectation values of antilinear operators.

Abstract

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call ``comb''. For qubits (or spin $1∕2$) the combs are automatically invariant under $\mathrm{SL}(2,\mathbb{C})$. This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulas for the concurrence and the three-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-qubit entanglement.