PIRSA:10070020

# Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration

### APA

Brandao, F. (2010). Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute. https://pirsa.org/10070020

### MLA

Brandao, Fernando. Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration. Perimeter Institute, Jul. 06, 2010, https://pirsa.org/10070020

### BibTex

```          @misc{ pirsa_10070020,
doi = {10.48660/10070020},
url = {https://pirsa.org/10070020},
author = {Brandao, Fernando},
keywords = {},
language = {en},
title = {Hasting{\textquoteright}s counterexamples on the minimum output entropy additivity conjecture by measure concentration},
publisher = {Perimeter Institute},
year = {2010},
month = {jul},
note = {PIRSA:10070020 see, \url{https://pirsa.org}}
}
```

Fernando Brandao California Institute of Technology (Caltech)

Talk Type

## Abstract

In 2008 Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture. In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. We prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension.