Apparantly this is possible, using some trickery:
Intel HD Graphics 4000 (Ivy Bridge)
Status: successful, 2560x1440 55 Hz tested
Tested with: Asus N56VM pre-sample and Fujitsu P27T-6 27-inch display with 2560x1440.
Instructions (Windows)
You need to manually add a new resolution to the Intel driver (Display -> Custom Resolutions) to use a resolution of 2560x1440 via HDMI. The driver complains that the bandwidth via HDMI is too low for a resolution of 2560x1440 at 60 Hz. With the "GTF" timing setting, only a maximum of 30 Hz was possible in our test. However, if you select "CVT-RB" (Reduced Blank) as Timing Standard, 2560x1440 at 55 Hz (55 p) is possible. But, it did not appear in the Windows dialog until we rebooted the computer. If it is still not listed after the first reboot, repeat the procedure.
If the image is distorted or flickers heavily, it might help to fiddle around with the monitor settings. E.g. the Fujitsu P27-T just stopped flickering in "Office" mode.
Linux (Ubuntu)
With the system tool of Linux only a maximum of 2560x1440 at 30 Hz (with noticeable delays) was possible. But, by means of a working windows configuration and PowerStrip you can also configure 2560x1440 at 55 Hz (with reduced blanking). Unfortunately, you can only specify modelines a multiple of 60 MHz at "reduced blanking" directly in the CVT tool.
2560x1440 30 Hz instructions:
The command
cvt 2560 1440 30
creates the appropriate modeline for xrandr, e.g. modeline "2560x1440_30.00" 146.25 2560 2680 2944 3328 1440 1443 1448 1468 -hsync +vsync
and you can add a new resolution with
xrandr --newmode "2560x1440_30.00" 146.25 2560 2680 2944 3328 1440 1443 1448 1468 -hsync +vsync
and one for HDMI2 with (for the name of the interface use xrandr without parameters)
xrandr --addmode HDMI2 "2560x1440_30.00"
2560x1440 55 Hz with reduced blanking
2560x1440 at 55 Hz: Thanks to X.Org FAQ we found a further solution. PowerStrip can display the currently used Linux modeline parameter. So, we could figure out the 55 MHz parameter that works with the P27T-6
xrandr --newmode "2560x1440" 220.812 2560 2608 2640 2720 1440 1443 1448 1478 -hsync -vsync
and activate it as usual with
xrandr --addmode HDMI2 "2560x1440"
Intel HD Graphics 3000 or Intel HD Graphics (Sandy Bridge)
Status: successful, 2560x1440 55Hz tested
Tested with: Acer Aspire TimelineU M3-581TG and Fujitsu P27T-6 27-inch display with 2560x1440.
Tested with: Intel Whitebook with Pentium B950 (HD Graphics) and Fujitsu P27T-6 27 inch display with 2560x1440.
Instructions
Same steps as for Intel HD Graphics 4000 (see above).
Source and further info: http://www.notebookcheck.net/2560x1440-or-2560x1600-via-HDMI.92840.0.html