Our pachysandra bed has been creeping into our lawn over the years. It has claimed about 2 feet of what used to be grass. I am in the process of digging out a 2 foot wide row. I plan to install some kind of barrier. Here is my question: how deep must this barrier be in order to foil the pachysandra spread?

I don't suppose I could encourage you to let the Pachysandra just take over the lawn?

Actually, Pachysandra is pretty shallow rooted. How far are you having to dig to reclaim the lawn? Probably not more than 6 inches. Less than that?
Your barrier has to be just a little deeper than the root system of the plant you are attempting to control. Worst case scenario for Pachysandra would be 7 inches.

Thanks @DaisyL