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)].

arXiv comment25 pages, comments are welcome!

References in corpus (27)

• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Bell inequalities for arbitrarily high dimensional systems
• Multidimensional quantum entanglement with large-scale integrated optics
• Testing the Hilbert space dimension
• Device-independent witnesses of genuine multipartite entanglement
• Robust Self Testing of the Singlet
• Maximally Non-Local and Monogamous Quantum Correlations
• No extension of quantum theory can have improved predictive power
• All Pure Bipartite Entangled States can be Self-Tested
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Device-independent entanglement quantification and related applications
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Robust and versatile black-box certification of quantum devices
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Self-testing of binary observables based on commutation
• Self-testing multipartite entangled states through projections onto two systems
• Bell inequalities tailored to maximally entangled states
• All the self-testings of the singlet for two binary measurements
• Self-testing protocols based on the chained Bell inequalities
• Scalable Bell inequalities for qubit graph states and robust self-testing
• Robust self testing of the 3-qubit $W$ state
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• Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism
• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Separation of quantum, spatial quantum, and approximate quantum correlations

Cited by in corpus (15)

• Non-locality sharing for a three-qubit system via multilateral sequential measurements
• An elegant proof of self-testing for multipartite Bell inequalities
• 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