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

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.

arXiv comment10 pages, 2 figures; Published version

References in corpus (40)

• Many-particle entanglement with Bose--Einstein condensates
• The Uncertainty Principle in the Presence of Quantum Memory
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• Entropic Uncertainty Relations and their Applications
• The Uncertainty Relation for Smooth Entropies
• Violation of local uncertainty relations as a signature of entanglement
• Entropic uncertainty relations - A survey
• Stronger uncertainty relations for the sum of variances
• Spin squeezing and pairwise entanglement for symmetric multiqubit states
• Quantum root-mean-square error and measurement uncertainty relations
• Multiqubit symmetric states with high geometric entanglement
• Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment
• Entanglement and symmetry in permutation symmetric states
• Variance-based uncertainty relations
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Majorana representation of symmetric multiqubit states
• Pairwise entanglement in symmetric multi-qubit systems
• Planar quantum squeezing and atom interferometry
• Experimental investigation of the stronger uncertainty relations for all incompatible observables
• Sum Uncertainty Relation in Quantum Theory
• Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
• A Stronger Multi-observable Uncertainty Relation
• Weighted Uncertainty Relations
• Bound entangled states violate a non-symmetric local uncertainty relation
• Uncertainty relations for general unitary operators
• Characterization of quantum angular-momentum fluctuations via principal components
• Entanglement robustness against particle loss in multiqubit systems
• Constraints on the uncertainties of entangled symmetric qubits
• State-independent preparation uncertainty relations
• Tight $N$-observable uncertainty relations and their experimental demonstrations
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Experimental investigation of multi-observable uncertainty relations
• Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit System
• SU(2) uncertainty limits
• State independent uncertainty relations from eigenvalue minimization
• Joint measurability, steering and entropic uncertainty
• Non-local properties of a symmetric two-qubit system
• Collective multipole-like signatures of entanglement in symmetric N-qubit systems
• Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors
• On Quantum Uncertainty Relations and Uncertainty Regions