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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.

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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:

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

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.

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yeah, i've since gotten myself some mDP to DP cables; those by Accell seem to work the best, since they don't connect the power pin; i'm still curious to know more about this HDMI thing, as some monitors don't have a DP connection – cnst May 7 '15 at 19:23
Well, my answer details that too. You need an active converter and you can go up to 4K@30z for now via a high speed cable. However you might need to use SwitchResX to tweak or force the resolutions you want as it doesn't always work the way you want it. – unmircea May 8 '15 at 11:56

Yes, supposedly, it is possible:

10ft 32AWG Mini DisplayPort to HDMI® w/Audio Cable - White

Supports "Dual Mode" input with a maximum resolution of 2560x1600

The mDP to HDMI cable above costs 7,50 USD, and explicitly clams to not be limited to 1080p.

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Actually cnst the link you provided clearly stated: > Note that this cable supports a maximum resolution of 1920x1080 when connected to a Mac computer. – warmth Jun 24 '14 at 2:12

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)?

If you mean with cheap: Passive adaptors which are usually sold cheap.
Then yes. Max output from the port will be 1920x1200.

If you mean with cheap: Cheapest active cable:
No. Display port can output much higher connections and 2560 × 1440 is not a problem. Plugging a cheap DP cable in a computer and in a laptop and things should just work. The only tricky part is if you have an old monitor which does not yet have DP. If you want to convert it then you need some axtive electronics (even though those can be hidden in a cable) and some output method which supports it. That can be the HDMI out.

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