# On the Variational Distance of Independently Repeated Experiments

## Renato Renner

```
```Let P and Q be two probability distributions which differ only
for values with non-zero probability. We show that the
variational distance between the distributions P^n and Q^n of
a series of n independently repeated random experiments
distributed according to P and Q, respectively, is upper
bounded by an expression which only grows like the square root
in n.