This display is connected through HDMI, I also tested Display Port with the
same result.

4K resolution is not detected and is not available in the display configuration
tool in Gnome 3.

Workaround:
Add the display mode manually and enable it with xrandr. The following
workaround doesn' t use optimal/accurate refresh rates/frequencies, it seems,
and should be used with caution, but I've been using it for several days on
such a display without problem (except some lag).

Source:
http://www.amazon.com/review/R3R4Y6PPZ1QN29/ref=cm_cr_dp_title?ie=UTF8&ASIN=B00BXF7I9M&nodeID=172282&store=electronics

Citation:

# cvt 3840 2160 13.8
# 3840x2160 13.79 Hz (CVT) hsync: 30.05 kHz; pclk: 144.25 MHz
Modeline "3840x2160_13.80" 144.25 3840 3944 4320 4800 2160 2163 2168 2180
-hsync +vsync
# xrandr --newmode "3840x2160_13.80" 144.25 3840 3944 4320 4800 2160 2163 2168
2180 -hsync +vsync
# xrandr --addmode HDMI1 "3840x2160_13.80"

Those make it so you can select it in the Displays or monitors section
depending on your distribution (make sure you have the right HDMI port by
running xrandr without any arguments).

If you don't know where the monitors section is you can run (leave off the
quotes):

xrandr --output HDMI1 --mode 3840x2160_13.80

I believe when using intel as a user, especially for on-processor
graphics like Haswell and Sandy, I got improved driver results when
using the latest microcode (video gfx acceleration is one. My i5 4670k
processor was new this year, and the latest microcode came out around
Aug 2013..  Gfx acceleration wasn't working with the packaged outdated
microcode of a few months older, but furthermore in order for me to use
proper working Haswell, I had to dive a bit into the testing branch, as
intel is making a lot of new work for it's latest HD-capable processors)

the command I use iucode-tool -K microcode.dat,

microcode.dat is inside tarballed file but is not usable for the
microcode service loader without extracting it  (you're pretty much
extracting the tarball which yields one file, then extracting/pulling an
arragenment of binary snippets for different processors from
microcode.dat, there's a way to extract just for your processor, if
interested for more elaboration, I made a post over here
https://plus.google.com/105696767572828808697/posts/fSMY3kT4c3s )

There's also this
https://01.org/linuxgraphics/community?qt-projects_aggregated_links=1
  ,but I would definitely include the processor type (eg, for me I'm
using an intel i5 "4670k".. The processor should be spottable somewhere
with dmidecode or cat /proc/cpuinfo (not sure if they can take debian
reports)

Hopefully this helps :)