Robust self testing of the 3-qubit $W$ state

Abstract

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit $W$ state, and show how to extend it to other pure three-qubit states. Our bounds are robust against the inevitable experimental errors.

arXiv comment9 pages, 2 figures

References in corpus (16)

• Three qubits can be entangled in two inequivalent ways
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Randomness vs Non Locality and Entanglement
• Robust Self Testing of the Singlet
• Device-independent entanglement quantification and related applications
• Robust and versatile black-box certification of quantum devices
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Family of Zeilinger-Horne-Greenberger "W" states lead to stronger nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states
• Device-independent certification of entangled measurements
• Testing the Structure of Multipartite Entanglement with Bell Inequalities
• Fusing multiple W states simultaneously with a Fredkin gate
• Device-independent tomography of multipartite quantum states

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