A post to the Diablo III forums by Blizzard community manager Vaeflare confirms presumptions that the recently announced version of Diablo III for the recently announced PlayStation 4 will not have any sort of cross-platform operability with the Windows edition of the action/RPG sequel:

While we think cross-platform play would be awesome, there are currently no plans to allow connectivity between PlayStation Network and Battle.net (this is pretty standard for most games that have PC and console support). As a result, the characters on your Battle.net account and PlayStation account will also remain separate.

In terms of allowing an analog controller hookup for the PC, we don’t have any plans for that kind of support right now. Similarly, since Diablo III for console was designed with a controller in mind, the PlayStation version of Diablo III will not support USB mice or keyboards.