Nonlocality and Entanglement for Symmetric States

Abstract

In this paper, building on some recent progress combined with numerical techniques, we shed some new light on how the nonlocality of symmetric states is related to their entanglement properties and potential usefulness in quantum information processing. We use semidefinite programming techniques to devise a device independent classification of three four qubit states into two classes inequivalent under local unitaries and permutation of systems (LUP). We study nonlocal properties when the number of parties grows large for two important classes of symmetric states: the W states and the GHZ states, showing that they behave differently under the inequalities we consider. We also discuss the monogamy arising from the nonlocal correlations of symmetric states. We show that although monogamy in a strict sense is not guaranteed for all symmetric states, strict monogamy is achievable for all Dicke states when the number of parties goes to infinity, as shown by an inequality based on a recent work studying the nonlocality (and showing strict monogamy) of W states.

13 pages, 5 figures. Added more physical perspectives including discussions about genuine nonlocality

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Cited by in corpus (14)

• Decoherence Effects on the Non-locality of Symmetric States
• Nonlocality of $W$ and Dicke states subject to losses
• The phases of the disordered Bose-Hubbard model with attractive interactions
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Deterministic Many-Resonator W Entanglement of Nearly Arbitrary Microwave States via Attractive Bose-Hubbard Simulation
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Bounding the persistency of the nonlocality of W states
• Logical and inequality based contextuality for qudits
• Symmetric quantum states: a review of recent progress
• Violation of generalized Bell inequality and its optimal measurement settings
• Revealing hidden physical nonclassicality with nonnegative polynomials
• All possible permutational symmetries of a quantum system
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Non-Gaussianity from superselection rules