There is no 4K profile for Blu-ray yet. Period. Not supported.
There’s apparently a group at the Blu-ray Disc Association studying the problem. That would presumably result in the definition of a new Blu-ray disc profile, as they did with BD Live!, BD Audio, 3D, etc.
This would not likely be directly compatible with today’s players. They might go to the existing BD-XL format, which supports 3 and 4 layer Blu-ray discs (so far, this is just a recording format, no one’s making glass mastered BD-XL discs). They might rather employ the HEVC video CODEC, rather than/in addition to AVC, since HEVC offers about twice the coding efficiency of AVC. And just when you thought those AVC rendering times were getting controllable.
Sony and Red are each currently offering 4K media players, the FMP-X1 and the RedRay, respectively. They’re not cheap, and they’re each using proprietary video CODECs. Red claims to be using only about 20Mb/s and a proprietary CODEC; Sony’s using H.264 today, but claim that HEVC/H.265 support will be forthcoming. They’re both concentrating on online rentals.
-Dave