Monogamous nature of symmetric N-qubit states of the W-class: Concurrence and Negativity Tangle

TL;DR

This paper investigates the monogamous entanglement properties of symmetric N-qubit W-class states using Majorana representation, revealing that concurrence tangle vanishes while negativity tangle captures residual entanglement.

Contribution

It demonstrates that for W-class states, concurrence tangle is zero, whereas negativity tangle effectively measures residual entanglement, highlighting differences in entanglement quantification methods.

Findings

Concurrence tangle vanishes for W-class states.

Negativity tangle is non-zero for W-class states.

Negativity tangle better captures residual entanglement.

Abstract

Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W-class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W-class of states is shown to be non-zero illustrating the fact that concurrence tangle underestimates the residual entanglement in a pure N-qubit state.