Can a Mini DisplayPort to HDMI cable support resolutions above 1920x1200?

Is it theoretically possible for a cheapo Mini DisplayPort to HDMI cable or adapter to support resolutions above 1920 × 1200, e.g. 2560 × 1440 (QHD)?

Or is it always electrically-equivalent to a single-link DVI, and such resolutions above 1920×1200 are out of the question?

From empirical evidence, I've tried out some rather expensive brand-name adapter from a local Apple dealer that was marked as HDMI 1.3 compliant with my mid-2013 MacBook Air (5000) and also with X230 (4000), and a QHD monitor, but was only getting a maximum of FHD resulution through such an arrangement.

Active DisplayPort (either normal or mini 1.1 or 1.2) to HDMI converters can go up to 3840x2160@30hz that's 4K@30hz. They use a Parade PS171 chip to achieve this, however it's not exactly plug and play on the Mac, you have to use SwitchResX. I'm told Windows works just fine on the same Mac hardware. (I'm using a 4K 40' Samsung 40HU6500 TV as a display)

Also make sure the HDMI cable is High-Speed.

See these:

http://www.delock.de/produkte/F_658_Displayport_62607/merkmale.html http://www.delock.de/produkte/F_658_Displayport_62611/merkmale.html

Later edit: Apparently mini Display Port 1.2 to HDMI 2.0 4k@60hz adapters are avaiable now, like this one from Clug 3D:

http://www.club-3d.com/index.php/products/reader.en/product/mini-displayport-12-to-hdmi-20-uhd-active-adapter.html

Later edit, however your Mac is newer than mine, I have a Macbook Pro Retina 13' late-2012, yours will do these resolutions directly over HDMI 1.3a, but it doesn't have a physical HDMI port, with a High Speed HDMI cable, and it should have DisplayPort 1.2, it could do 4K@60hz easily but there are no converters for that yet, essentially you need to connect it directly via DisplayPort.

Which I think is what you want, IF your monitor has DisplayPort input just buy a miniDisplayPort (Thunderbolt) to DisplayPort Female adapter, this is very cheap and you get any resolution you wish.

http://amzn.com/B00HNF0KF0

http://www.delock.de/produkte/F_1293_Mini-Displayport-Stecker---Displayport-Buchse_65554/merkmale.html

https://www.google.ro/search?q=mini+displayport+to+displayport+female