A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy Ii: Convexity and Concavity
نویسندگان
چکیده
We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Φp,q(A1, A2, . . . , Am) = (
منابع مشابه
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
and prove that it is jointly concave for 0 < p ≤ 1 and convex for p = 2. We then derive from this a Minkowski type inequality for operators on a tensor product of three Hilbert spaces, and show how this implies the strong subadditivity of quantum mechanical entropy. For p > 2, Φp is neither convex nor concave. We conjecture that Φp is convex for 1 < p < 2, but our methods do not show this. ∗ Wo...
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