Current gen barely gets 1080p but with much better lighting , textures, effects and antialiasing over a PS3. If the GPU is 8 times stronger than the PS4 as Captain_Tom points out, then it would have arround 1.84 x 8 or 15 Teraflops of computing power. If a Geforce GTX 980 or a Radeon R9 290X is playing 4K (mid to high quality, not ultra) and have arround 5 Teraflops and 240-320 GB/s bandwith, then a 15 Teraflops GPU with 1 TB/s Bandwith would be enough for 4k mantaining the quality of actual textures. I dont know if it can be done at 400 USS.
Currently, you don't know if it could be done currently. By the next release, probably