Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

TL;DR

This paper demonstrates that violations of local sum uncertainty relations for angular momentum operators in bipartite permutation symmetric systems indicate entanglement, linking these violations to covariance matrix negativity in symmetric multi-qubit states.

Contribution

It establishes a direct connection between LSUR violations and entanglement detection in symmetric multi-qubit systems, extending previous criteria.

Findings

Violation of LSUR indicates entanglement in symmetric states

LSUR violation correlates with covariance matrix negativity

Provides a criterion for entanglement detection in symmetric qubits

Abstract

We show that violation of variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi~[Phys.Rev.A {\bf 68}, 032103 (2003)], reflects entanglement in the equal bipartitions of an $N$-qubit symmetric state with even qubits. We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix [Phys. Lett. A, {\bf 364}, 203 (2007)] of the two-qubit reduced system of a permutation symmetric $N$-qubit state.