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

References in corpus (22)

• Device-independent security of quantum cryptography against collective attacks
• Hacking commercial quantum cryptography systems by tailored bright illumination
• Multi-party entanglement in graph states
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Experimental entanglement of six photons in graph states
• Device-independent quantum key distribution secure against collective attacks
• Bounding the set of quantum correlations
• Secure device-independent quantum key distribution with causally independent measurement devices
• Private Randomness Expansion With Untrusted Devices
• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• Experimental entanglement of a six-photon symmetric Dicke state
• Bell Inequalities for Graph States
• The geometric measure of entanglement for symmetric states
• Generalized Flow and Determinism in Measurement-based Quantum Computation
• The maximally entangled symmetric state in terms of the geometric measure
• All entangled pure states violate a single Bell's inequality
• Monogamy of Bell's inequality violations in non-signaling theories
• Inert states of spin-S systems
• Mermin inequalities for perfect correlations
• Persistency of entanglement and nonlocality in multipartite quantum systems
• Experimentally implementable criteria revealing substructures of genuine multipartite entanglement