Nonlocality of Symmetric States

Abstract

In this paper we study the non-local properties of permutation symmetric states of n-qubits. We extend the bipartite Hardy paradox and the associated CH-inequality to n-party permutation symmetric states to show that all symmetric states exhibit non-locality. Natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different non-local features. We define inequalities which are violated by all states of one entanglement class, whereas there are states outside that class which do not violate.

arXiv comment4 pages of main text + 5 pages of proofs. 1 figure

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• Optimal quantum tomography of permutationally invariant qubits
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• Nonlocality of $W$ and Dicke states subject to losses
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Increased success probability in Hardy's nonlocality: Theory and demonstration
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• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Necessary and sufficient conditions for local creation of quantum discord
• Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models
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• On Possibilistic Conditions to Contextuality and Nonlocality
• Symmetric quantum states: a review of recent progress
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• Characterizing nonlocality of pure symmetric three-qubit states
• Sheaf-Theoretic Methods in Quantum Mechanics and Quantum Information Theory
• Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
• A Logical Proof of Quantum Correlations Requiring Entanglement Measurements
• All possible permutational symmetries of a quantum system
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Stellar representation of extremal Wigner-negative spin states
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states