Family of Bell inequalities violated by higher-dimensional bound entangled states

Abstract

We construct ($d\times d$)-dimensional bound entangled states, which violate, for any $d>2$, a bipartite Bell inequality introduced in this paper. We conjecture that the proposed class of Bell inequalities acts as a dimension witness for bound entangled states: For any $d>2$ there exists a Bell inequality from this class that can be violated with bound entangled states only if their Hilbert space dimension is at least $d\times d$. Numerics supports this conjecture up to $d=8$.

13 pages, 1 figure

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Cited by in corpus (9)

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• A class of genuinely high-dimensionally entangled states with a positive partial transpose
• Bound entangled states are useful in prepare-and-measure scenarios
• Bipartite Bound Entanglement
• Extended Bell inequality and maximum violation
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Measuring outcome correlation for spin-s Bell cat-state and geometric phase induced spin parity effect
• Unlimited quantum correlation advantage from bound entanglement