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Strong subadditivity of entropy: when is it (nearly) saturated?

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If you have a question about this talk, please contact Ashley Montanaro.

Strong subadditivity of the quantum entropy (Lieb, Ruskai 1973) is the fundamental inequality, used over and over again in quantum information and many-body physics. It states that for any state rho on three parties A, B, C,

I(A:C|B) := S(AB)+S(BC)-S(B)-S(ABC) >=0. (SSA)

In joint work with Hayden, Jozsa and Petz, we had clarified the structure of states saturating SSA . I will review this result, which in particular implies that for such states, rho_AC has to be separable. What can be said about the case when I(A:C|B) is “small”? After reviewing the situation in the classical case, i formulate a general form for a conjectured stronger subadditivity relation. Its simplest form turns out to be false. However, if some version of it holds, this would have very interesting consequences: it would imply that rho_AC is k-extendible, where k is an anti-monotonic function of I(A:C|B). This would extend and complement results by Brandao, Christandl and Yard (arXiv:1011.2751) regarding the faithfulness of squashed entanglement.

This talk is work in progress with Ke Li.

This talk is part of the CQIF Seminar series.

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