Complete proof of Gisin's theorem for three qubits

Abstract

Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.

Revised version with minor corrections in typos, written in double column format, 4 pages, Latex

References in corpus (4)

• Proofs of nonlocality without inequalities revisited
• Multipartite Bell-type inequalities for arbitrary numbers of settings and outcomes per site
• Bell inequalities for three particles
• Joint Probabilities Reproducing Three EPR Experiments On Two Qubits

Cited by in corpus (14)

• All entangled pure states violate a single Bell's inequality
• Generalized Hardy's Paradox
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• Identification of three-qubit entanglement
• Bell inequalities for multipartite qubit quantum systems and their maximal violation
• Multipartite Bell-type Inequality by Generalizing Wigner's Argument
• Genuine multipartite nonlocality in the one-dimensional ferromagnetic spin-1/2 chain
• True Multipartite Entanglement Hardy Test
• Hierarchy of multipartite nonlocality in the nonsignaling scenario
• Certification of Genuine Multipartite Entanglement with General and Robust Device-independent Witnesses
• Chain of Hardy-type local reality constraints for $n$ qubits
• Balanced Tripartite Entanglement, the Alternating Group A4 and the Lie Algebra $sl(3,C)\oplus u(1)$
• The Hardy's nonlocality argument
• Testing Genuine Multipartite Nonlocality via an Inflated Network with Multi-copy Entangled States