Increasing the statistical significance of entanglement detection in experiments

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Indeed, with the given choice of observables the operators ℬ M \mathcal{B}_{\rm M} and ℬ A \mathcal{B}_{\rm A} are identical within quantum mechanics. However, the use of A A and B B within the Ardehali inequality results in a more restrictive test for LHV models

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In Ref. [ 10 ] the second term, − ⟨ ℳ ⟩ / n tot -\langle{\mathcal{M}}\rangle/n_{\rm tot} , is omitted, leading to a systematic overestimation of the standard deviation. Such an overestimation is problematic, if the claim is that certain state properties (e.g. having a negative partial transpose) are not significant. This can occur, e.g. in the analysis of bound entanglement, see A. Elias and M. Bourennane, Nature Phys. 5

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