Constraints on the uncertainties of entangled symmetric qubits

Abstract

We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states. Pairwise entangled symmetric multiqubit states are shown here to obey these constraints. We also bring out an elegant local invariant structure exhibited by our constraints.

5 pages, REVTEX, Improved presentation; Theorem on neccessary and sufficient condition included; To appear in Phys. Lett. A

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• Spin squeezing and entanglement
• Covariance matrices and the separability problem
• Entanglement and permutational symmetry
• Separability criteria and entanglement witnesses for symmetric quantum states
• Partial transpose criteria for symmetric states
• Optimal quantum tomography of permutationally invariant qubits
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• Collective randomized measurements in quantum information processing
• Truncated su(2) moment problem for spin and polarization states
• Collective multipole-like signatures of entanglement in symmetric N-qubit systems
• Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach
• Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics
• Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors
• Minimum Uncertainty and Entanglement
• Equivalence of classicality and separability based on P phase-space representation of symmetric multiqubit states
• The relation between nonlocality and contextuality for a biphoton
• Spin squeezing in Dicke-class of states with non-orthogonal spinors
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Visualisation of an entangled channel spin-1 system
• Lorentz invariants of pure three-qubit states