QLunch: The catalytic entropy conjecture
Speaker: Henrik Wilming, ETH Zurich
Title: The catalytic entropy conjecture
The von Neumann entropy is a key quantity in quantum information theory and, roughly speaking, quantifies the amount of quantum information contained in a state in the asymptotic regime, where many identically and independently distributed (i.i.d.) copies of the state are available. I will discuss recent operational characterizations of the von Neumann entropy which neither require an i.i.d. limit nor any explicit randomness. Instead, they build on the notion of catalysts - ancillary systems that can be re-used after they helped to implement a state transition. The simplest such characterization leads to the "catalytic entropy conjecture", which gives an elegant single-shot characterization of von Neumann entropy.
I will present some results providing evidence in favor of the conjecture and discuss the difficulties that one encounters when trying to prove it.
These are closely linked to the structure of multi-partite correlations and lead to some interesting side-results, in particular a simple way to understand the difference between general unital quantum channels and random unitary channels in terms of "catalytic dilations".