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Minimum quantum resources for strong non-locality
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We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non-LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreasing entanglement between one qubit and the other two, necessitating an increasing number of local measurements on the latter.
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Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications
AMCCs are introduced as the correlation-space analogue of absolutely maximally entangled states, with PR boxes, GHZ correlations, and parity/CSP-built families as examples.
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