Theory Seminar: Single-shot interpretations of von Neumann entropy

Henrik Wilming (ETH Zürich)
In quanum information theory, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by (smoothed) Renyi entropies.

Henrik Wilming (ETH Zürich)
Herbert-Walther Lecture Hall G0.25
Wed 13. February 2019, 11:30 am (MEZ)

 

Abstract:

In quanum information theory, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by (smoothed) Renyi entropies. I discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. First, I present results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space. Then I show that the von Neumann entropy governs single-shot transitions whenever one has access to arbitrary auxiliary systems, which have to remain invariant in a state-transition ("catalysts"), as well as a decohering environment. Getting rid of the decohering environment yields the "catalytic entropy conjecture", for which I present some supporting evidence. I also discuss applications to thermodynamics.