Observables suitable for restricting the fidelity to multipartite maximally entangled states

Abstract

We present a class of observables which are suitable for determining the fidelity of a state to the multipartite Greenberger-Horne-Zeilinger (GHZ) state. Given an expectation value of an observable belonging to the class, we give a simple formula that gives a lower bound and an upper bound for the fidelity. Applying the formula to the GHZ-state preparation experiment by Pan {\it et al}. {[Nature (London) {\bf 403}, 515 (2000)]}, we show that the observed state lies outside of the class of biseparable mixed three-qubit states. We also show that for this class of operators, adopting the principle of minimum variance {[Phys. Rev. A {\bf 60}, 4338 (1999)]} in the state estimation always results in the state with the minimum fidelity.

6 pages

References in corpus (3)

• Classification of mixed three-qubit states
• Experimental Four-photon Entanglement and High-fidelity Teleportation
• Sufficient conditions for three-particle entanglement and their tests in recent experiments

Cited by in corpus (10)

• Entanglement detection
• Partial separability and entanglement criteria for multiqubit quantum states
• Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon
• Configuration of separability and tests for multipartite entanglement in Bell-type experiments
• Kochen-Specker theorem as a precondition for secure quantum key distribution
• Efficient decoherence-free entanglement distribution over lossy quantum channels
• Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"
• Inequalities for experimental tests of the Kochen-Specker theorem
• Experimental entanglement swapping through single-photon ${\chi }^{(2)}$ nonlinearity
• Additional information decreases the estimated entanglement using the Jaynes principle