Monotonicity under local operations: Linear entropic formulas

Presenting Author: Mohammad Alhejji, National Institute of Standards and Technology, Boulder
Contributing Author(s): Graeme Smith

All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a physical system which has n parts. We show that these formulas form a polyhedral convex cone, which we call the monotonicity cone, and enumerate its facets. We illustrate its structure and prove that it is equivalent to the cone of monotonic formulas implied by strong subadditivity. We explicitly compute its extremal rays for n up to 5. We also consider the symmetric monotonicity cone, in which the formulas are required to be invariant under subsystem permutations. We describe this cone fully for all n.

Read this article online: https://www.dropbox.com/s/r1odnqr1fuhcmz1/Paper_2018-1109GS.pdf?dl=0

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