A generalization of the CHSH inequality self-testing maximally entangled states of any local dimension

Abstract

For every $d\ge 2$, we present a generalization of the CHSH inequality with the property that maximal violation self-tests the maximally entangled state of local dimension $d$. This is the first example of a family of inequalities with this property. Moreover, we provide a conjecture for a family of inequalities generalizing the tilted CHSH inequalities, and we conjecture that for each pure bipartite entangled state there is an inequality in the family whose maximal violation self-tests it. All of these inequalities are inspired by the self-testing correlations of [Nat. Comm. 8, 15485 (2017)].

arXiv comment10 pages, added robust self-testing bounds

References in corpus (16)

• Fully device independent quantum key distribution
• Randomness vs Non Locality and Entanglement
• Robust Self Testing of the Singlet
• All Pure Bipartite Entangled States can be Self-Tested
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Quantum Random Access Codes using Single $d$-level Systems
• Robustness and device independence of verifiable blind quantum computing
• Bell inequalities tailored to maximally entangled states
• Interactive proofs for BQP via self-tested graph states
• Causality and Cirel'son bounds
• Robust self-testing of many-qubit states
• Self-testing in parallel
• Test for a large amount of entanglement, using few measurements
• Robust self-testing for linear constraint system games
• The Parallel-Repeated Magic Square Game is Rigid
• Separation of finite and infinite-dimensional quantum correlations, with infinite question or answer sets

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• Bell inequalities tailored to the Greenberger-Horne-Zeilinger states of arbitrary local dimension
• Custom Bell inequalities from formal sums of squares
• Maximal Violation of a Broad Class of Bell Inequalities and Its Implications on Self-Testing
• Parallel Self-Testing of the GHZ State with a Proof by Diagrams
• Self-testing quantum systems of arbitrary local dimension with minimal number of measurements
• Experimental self-testing for photonic graph states
• Separation of quantum, spatial quantum, and approximate quantum correlations
• On the Fidelity Robustness of CHSH--Bell Inequality via Filtered Random States
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• Engineering entanglement and teleportation via solving Lindblad master equation
• Impossibility of adversarial self-testing and secure sampling