Beyond the entanglement of qubit pair in a mixed state

TL;DR

This paper investigates the distribution of entanglement in multipartite qubit systems, deriving monogamy constraints that relate various entanglement measures and help identify multipartite entanglement from two-qubit access.

Contribution

It introduces algebraic monogamy constraints linking one-tangle, two-tangles, and three-tangles in N-qubit states, advancing understanding of entanglement distribution.

Findings

Derived monogamy relations between entanglement measures.

Provided criteria for detecting multipartite entanglement.

Analyzed constraints for N-qubit pure states.

Abstract

Given a multipartite quantum system that consists of two-level particles (qubits), one may or may not have access to all the subsystems. What can we know about the entanglement of the multiqubit system and residual correlations beyond two-tangle if we have access only to two-qubits at a time? Algebraic analysis of two-qubit states yields monogamy constraints on distribution of entanglement between sub-systems of an N-qubit state and criterion to determine if the state has multipartite entanglement. Monogamy constraints, reported in this letter, are relations between well known entanglement measures such as one-tangle, two-tangles and three-tangles of an N-qubit pure state.