Papers › Information theoretical perspective on the method of Entanglement Witnesses

Information theoretical perspective on the method of Entanglement Witnesses

15 Aug 2023arXiv:2308.07744links table onlyarchive 2025-07-28

Paulo J. Cavalcanti, Giovanni Scala, Antonio Mandarino, Cosmo Lupo

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We frame entanglement detection as a problem of random variable inference to introduce a quantitative method to measure and understand whether entanglement witnesses lead to an efficient procedure for that task. Hence we quantify how many bits of information a family of entanglement witnesses can infer about the entanglement of a given quantum state sample. The bits are computed in terms of the mutual information and we unveil there exists hidden information not \emph{efficiently} processed. We show that there is more information in the expected value of the entanglement witnesses, i.e. 𝔼[W]=⟨W ⟩ᵨ than in the sign of 𝔼[W]. This suggests that an entanglement witness can provide more information about the entanglement if for our decision boundary we compute a different functional of its expectation value, rather than sign(𝔼[ W ]).

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