Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party

Abstract

Device independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks but also their implications towards foundations of quantum theory. The strongest form of device independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently in [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide the first self-testing scheme for the multipartite Greenberger-Horne-Zeilinger (GHZ) states of arbitrary local dimension that does not rely on self-testing results for qubit states and that exploits the minimal number of two measurements per party. This makes our results interesting as far as practical implementation of device-independent certification methods is concerned. Our self-testing statement relies on maximal violation of a Bell inequality proposed recently in [R. Augusiak et al., New J. Phys. 21, 113001 (2019)].

25 pages, comments are welcome!

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• Device-independent security of quantum cryptography against collective attacks
• Testing the Hilbert space dimension
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• No extension of quantum theory can have improved predictive power
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
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• Custom Bell inequalities from formal sums of squares
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Certification of the maximally entangled state using non-projective measurements
• Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Deriving three-outcome permutationally invariant Bell inequalities
• A universal scheme to self-test any quantum state or measurement
• Model-independent inference of quantum interaction from statistics
• Self-testing composite measurements and bound entangled state in a single quantum network
• Almost device-independent certification of GME states with minimal measurements
• Supersinglets can be self-tested with perfect quantum strategies
• Topologically noise robust network steering without inputs
• Any gate of a quantum computer can be certified device-independently
• Robust self-testing and certified randomness based on chained Bell inequality