The concept of a deep image isn’t brand new; ultimately it’s just the technique of encoding more than just the RGBA value in a pixel. Many applications and systems already store multiple channels of data to enhance the compositing workflow as well as re-using calculations already performed by the rendering engine. Side FX software’s Houdini is an example of one of the more recent applications to utilize this workflow via it’s custom camera image format.
What we’re doing is utilizing a simplification of already existing representations for shadow maps to encode camera space information. This reaches further than traditional Z depth buffers, as those tend to lead to artifacts in semi transparent areas, such as motion blur or oversampling.
Deep images solve this issue by storing multiple samples for every pixel at varying depths which contain the chosen values (opacity, color, P) at that depth, encoding it in efficient way to solve a lot of the aforementioned historical issues.

Collection of Pixar Scientific Papers from Siggraph and other Pixar presentations. Going as far back as 1982's presentation of the Cook-Torrance shading model.

The following are some very interesting insights on filtering in PRMan.