Abstract

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.