Single-shot interpretations of von Neumann entropy (Henrik Wilming)
Feb 13, 2019
Max Planck Institute of Quantum Optics
Hörsaal, Raum B 0.32 / New lecture hall, Room B 0.32
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.