I've recently bought brand new ASUS PB278Q monitor.
When trying to connect to my laptop, everything works great, except that I can't get the native resolution of my monitor (2560x1440) working. The automatic is 1920x1080.
My graphic card is Nvidia GeForce 320m.
Here's output from lspci for it:

~$ lspci | grep VGA
02:00.0 VGA compatible controller: NVIDIA Corporation GT216M [GeForce GT 320M] (rev a2)

and also xrandr:

~$ xrandr
Screen 0: minimum 8 x 8, current 3286 x 1437, maximum 8192 x 8192
VGA-0 disconnected (normal left inverted right x axis y axis)
LVDS-0 connected primary 1366x768+0+669 (normal left inverted right x axis y axis) 344mm x 193mm
   1366x768       60.0*+
HDMI-0 connected 1920x1080+1366+0 (normal left inverted right x axis y axis) 600mm x 340mm
   1920x1080      60.0*+   59.9     50.0     30.0     25.0     24.0     60.0     50.0  
   1680x1050      60.0  
   1440x900       59.9  
   1280x1024      75.0     60.0  
   1280x960       60.0  
   1280x800       59.8  
   1280x720       60.0     59.9     50.0  
   1152x864       75.0  
   1024x768       75.0     70.1     60.0  
   800x600        75.0     72.2     60.3     56.2  
   720x576        50.0  
   720x480        59.9  
   640x480        75.0     59.9     59.9  
   480x576        50.0  
   480x480        59.9  

I have proprietary drivers installed on my machine, here's the info about the monitor from nvidia-settings (Actually I don't have enough reputation to post images, so here's the text):

Chip Location: Internal
Signal: TDMS
Connection link: Single
Native resolution: 2560x1440
Refresh rate: 60.00 Hz

The monitor is connected to laptop via HDMI cable, and honestly I have no idea what version it is, and what version is my HDMI output of my graphics card. I tried to find how I can figure it out on the web, but had no luck. Also my video card has only VGA and HDMI outs so I can't test neither DVI-D cable nor DisplayPort.

So apparently, there's some problem over there. At least I want to know exactly what's going on. I've tried to see if it a linux-specific problem, but windows also gave me the same resolution by default.

What I've already tried:

1. Connect through VGA (stupid one, of course it gave me 1920x1080).
2. Checked two HDMI cables (not sure if they're the same or not, as mentioned above).
3. Played around with xrandr and adding custom modes. Didn't help.
4. Surfed for the info a lot on the web, but couldn't get appropriate results.

Actually xrandr gives me the following:

~$ cvt 2560 1440 60
# 2560x1440 59.96 Hz (CVT 3.69M9) hsync: 89.52 kHz; pclk: 312.25 MHz
Modeline "2560x1440_60.00"  312.25  2560 2752 3024 3488  1440 1443 1448 1493 -hsync +vsync
~$ xrandr --newmode "2560x1440_60.00"  312.25  2560 2752 3024 3488  1440 1443 1448 1493 -hsync +vsync
~$ xrandr
Screen 0: minimum 8 x 8, current 3286 x 1437, maximum 8192 x 8192
VGA-0 disconnected (normal left inverted right x axis y axis)
LVDS-0 connected 1366x768+0+669 (normal left inverted right x axis y axis) 344mm x 193mm
   1366x768       60.0*+
HDMI-0 connected primary 1920x1080+1366+0 (normal left inverted right x axis y axis) 600mm x 340mm
   1920x1080      60.0*+   59.9     50.0     30.0     25.0     24.0     60.0     50.0  
   1680x1050      60.0  
   1440x900       59.9  
   1280x1024      75.0     60.0  
   1280x960       60.0  
   1280x800       59.8  
   1280x720       60.0     59.9     50.0  
   1152x864       75.0  
   1024x768       75.0     70.1     60.0  
   800x600        75.0     72.2     60.3     56.2  
   720x576        50.0  
   720x480        59.9  
   640x480        75.0     59.9     59.9  
   480x576        50.0  
   480x480        59.9  
  2560x1440_60.00 (0x34f)  312.2MHz
        h: width  2560 start 2752 end 3024 total 3488 skew    0 clock   89.5KHz
        v: height 1440 start 1443 end 1448 total 1493           clock   60.0Hz
~$ xrandr --addmode HDMI-0 2560x1440_60.00
X Error of failed request:  BadMatch (invalid parameter attributes)
  Major opcode of failed request:  140 (RANDR)
  Minor opcode of failed request:  18 (RRAddOutputMode)
  Serial number of failed request:  29
  Current serial number in output stream:  30

What I intend to do next:

1. Try another HDMI cable?
2. Try HDMI to DVI-D cable?
3. Try HDMI to DisplayPort cable?
4. Another type of adapters? VGA to DVI-D?
5. Buy another laptop with another graphic card. Damn.
6. My ideas pretty much end here.

Any ideas?
Any explanations why it isn't working are appreciated.