On Strong Monogamy Conjecture in Four-Qubit System

TL;DR

This paper extends the strong monogamy inequality to negativity in four-qubit systems, analyzing its validity on pure states, providing classes of states satisfying it, and identifying cases of violation.

Contribution

It generalizes the strong monogamy relation to negativity and offers detailed analysis and classes of states where it holds or fails in four-qubit systems.

Findings

Negativity satisfies strong monogamy in certain four-qubit states.

Identified classes of states where strong monogamy is valid.

Found cases where strong monogamy is violated.

Abstract

Monogamy is a defining feature of entanglement, having far reaching applications. Recently, Regula \textit{et.al.} in Phys. Rev. Lett. \textbf{113}, 110501(2014) have proposed a stronger version of monogamy relation for concurrence. We have extended the strong monogamy inequality for another entanglement measure, viz., negativity. In particular, we have concentrated on four-qubit system and provided a detail study on the status of strong monogamy on pure states. Further, we have analytically provided some classes of states for which negativity and squared negativity satisfy strong monogamy. Numerical evidences have also been shown in proper places. Our analysis also provides cases where strong monogamy is violated.