Negativity Fonts, multiqubit invariants and Four qubit Maximally Entangled States

TL;DR

This paper introduces negativity fonts as fundamental units of multipartite entanglement, deriving invariants for four-qubit states and analyzing their entanglement features through determinants and numerical evaluations.

Contribution

It develops a framework linking negativity fonts to LU invariants and provides new invariants for four-qubit entanglement analysis, including their relation to known maximally entangled states.

Findings

Derived expressions for global negativity in terms of negativity font determinants.

Constructed LU invariants of degree four and six for four-qubit states.

Numerical analysis reveals features of maximally entangled four-qubit states.

Abstract

Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N- qubit state and linear entropy of reduced single qubit state yields an expression for global negativity in terms of determinants of negativity fonts. Transformation equations for determinants of negativity fonts under local unitaries (LU's) are useful to construct LU invariants such as degree four and degree six invariants for four qubit states. The difference of squared negativity and N-tangle is an N qubit invariant which contains information on entanglement of the state caused by quantum coherences that are not annihilated by removing a single qubit. Four qubit invariants that detect the entanglement of specific parts in a four qubit state are expressed in terms of three qubit subsystem invariants. Numerical values of invariants bring out distinct features of several four qubit states which have been proposed to be the maximally entangled four qubit states.