Relation between entanglement measures and Bell inequalities for three qubits

Abstract

For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence $\mathcal{C}$) and the maximal violation $\mathcal{M}$ of a Bell inequality. No such relation exists for the three-qubit analogue of $\mathcal{C}$ (the tangle $\tau$), but we have found that numerical data is consistent with a simple set of upper and lower bounds for $\tau$ given $\mathcal{M}$. The bounds on $\tau$ become tighter with increasing $\mathcal{M}$, so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can be tightened further if the tangle is replaced by an entanglement monotone that can identify both the W state and the Greenberger-Horne-Zeilinger state.

3 pages, 2 figures

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• Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states
• Gisin's Theorem for Three Qubits
• Quantifying Quantum Coherence in Experimentally-Observed Neutrino Oscillations
• Genuine multipartite entanglement measure
• Numerical evaluation of convex-roof entanglement measures with applications to spin rings
• Concurrence triangle induced genuine multipartite entanglement measure
• The n-tangle of odd n qubits
• Tripartite entanglement measure under local operations and classical communication
• A bipartite class of entanglement monotones for N-qubit pure states
• Nonlocality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Efficient Test to Demonstrate Genuine Three Particle Nonlocality
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• Tight upper bound for the maximal expectation value of the Mermin operators
• Experimental verification of time-order-dependent correlations in three-qubit Greenberger-Horne-Zeilinger-class states
• Efficient creation of multipartite entanglement in flux qubits
• Detection of Genuine Multipartite Entanglement in Arbitrary Multipartite systems
• Distribution of Non-Locality On Quantum Random Circuits
• Analysing the efficiency of partially entangled states in Vaidman's-type games and its applications in Quantum Secret Sharing