Can a premium HDMI cable outperform a standard cable?

You would do a BERT (bit error rate test) on the cable. Better yet, look at the eye diagram at the far end of the cable.

HDMI is a digital format, which means that there's a threshold effect — cable quality does not affect the picture quality at all until it gets so bad that it actually causes bit errors.

"Premium" cable is (supposedly) built to tighter tolerances (reduced ISI), with thicker wire (reduced attenuation) and/or with better shielding (reduced external interference) so that you can have longer runs of it before that starts to happen.

Bit errors flip individual bits, and the visual effect depends on exactly what that bit is used for. A bit error in one of the MSBs of a color channel will cause a pixel to be unexpectedly brighter or darker than it should be — this is commonly called "salt and pepper noise" because in a B&W system, the random white and black pixels look like salt and pepper have been sprinkled on the image.

HDMI cables are tested at an Authorized Testing Center (ATC) and given a certification based on how much bandwidth they can handle (which is to say, how high of a frequency signal they can transmit without the signal degrading beyond some parameters specified in the standard).

Signals in a cable degrade. The signal that is input to the cable is not precisely the same as the signal that is received, due to various effects which depend chiefly on cable length, the physical properties of the cable stock, and the signal frequency. The longer the cable is, the more distorted the signal will be, and the worse the cable stock is, the more distorted the signal will be per meter of cable that it passes through.

In analog signaling, any amount of distortion changes the image, it's just a question of by how much. If we're transmitting an image across, say, a VGA cable, then you have 3 signal lines, one for each channel of a pixel (red, green, and blue). Each pixel is transmitted in sequence, and the voltage on each line at any given time represents the brightness of one channel of the current pixel. I don't know what the signal voltage of VGA is, but I'm going to pretend it's 1.0 V. Since it's analog, if the signal voltage is 0, that means 0 brightness, if it's 1 V, that means 100% brightness, 0.5 V means 50% brightness, etc. The voltage on the line is analagous to the value being communicated. Of course, if you transmit 0.55 V and, due to distortion, the receiver picks up 0.51 V, the image will come out ever so slightly different than intended. And more distortion means larger inaccuracy in the results.

In digital signaling, nothing changes, except that we only signal 0 V or 1 V. We don't use any of the inbetween voltage levels (some digital signals will use several levels, maybe 4 or 5 levels instead of 2, but the point is, we only use a few levels instead of a continuous spread. For simplicity, we'll go ahead with just 2-level digital signaling). Since we are not using any inbetween levels, the receiver knows automatically that if it receives a 0.8 V or a 0.9 V signal, that it is really supposed to be a 1 V. So, distortion is corrected by the receiving device. Of course, there is a trade-off, since you can only represent 2 different numbers with each signal instead of dozens or hundreds, you require many additional signal cycles in order to communicate the same amount of information. That's why a 3-channel analog video system like VGA only needs to operate at around 150 MHz on each channel to transmit 1080p 60 Hz, while a comparable digital equivalent like HDMI (which also uses 3-channels, one for each color channel in RGB mode) has to operate at around 1.5 GHz on each channel to transmit 1080p 60 Hz. But anyway...

So distortion in the signal has no effect on the image quality of a digital transmission, because even though the voltages of the signal might be altered slightly during transmission, the system can tell what it was supposed to be, as long as it's even remotely close to the intended value. However, it's important to note that digital signals aren't immune to interference. The only difference is that the effects of the interference are corrected by the receiver.

Because of this ability to correct interference, the quality of an image transmitted over a digital interface like HDMI is not affected by the cable, as long as the distortion is small enough to be correctable. Different HDMI cables do have different amounts of signal distortion, but since the distortion is corrected, it's irrelevant, UNLESS the distortion is so high that the receiver starts interpreting values incorrectly. So how does that happen? Well like I said, the distortion in the cable is affected by the cable length, cable stock quality, and signal frequency. That means:

• (Mainly applicable to manufacturers) For a given signal and cable stock, if you make longer and longer cables from that stock, the signal will eventually fail to transmit correctly. In this case, you would need a better quality cable stock if you wanted to make a cable of that length that can handle that signal
• (Again mainly a consideration for cable manufacturers) For a given signal and cable length, if you make the cable out of shitty enough cable stock, it will fail to transmit correctly. However, that cable stock may work for shorter cables, and it will also likely work for lower frequency transmissions, so you can simply label it with a lower rated speed and sell it
• (This is applicable to consumers) For a given cable, with a certain length and construction, if you signal at higher and higher frequencies, eventually it will fail to transmit correctly. So a cable that is ok at 10.2 Gbit/s may not work at 18 Gbit/s. To transmit at the higher signal frequency, you would need either a higher quality cable or a shorter cable, or some combination of the two.

If you have a cable and you transmit higher and higher frequencies, you won't get decreased image quality, it will just fail to work once you pass a certain point (or, it will work intermittently, if you are right up against the limits).

In realistic terms, pretty much any HDMI cable can handle 10.2 Gbit/s (1080p 144 Hz or 1440p 75 Hz, or 4K 30 Hz), and even 18 Gbit/s (4K 60 Hz) at shorter lengths, no matter how cheap the cable stock used by the manufacturer. However, when you start combining long cable lengths and high frequencies (i.e. if you want a 15 meter cable for 4K 60 Hz, requiring 18 Gbit/s), you will get failures if the cable is not a high enough quality.

But, it's not really a big deal. Because the creators of the HDMI have certifications for certain thresholds of bandwidth.

Cables that have been tested at an Authorized Testing Center to reliably handle signals with fundamental frequencies of up to 3.4 GHz on each channel (i.e. 10.2 Gbit/s aggregate, or the maximum speed of HDMI 1.3/1.4) are given a High Speed HDMI cable certification.

Cables that have been tested at an ATC to reliably handle signals up to 6.0 GHz per channel on 3 channels (i.e. 18.0 Gbit/s, or maximum speed of HDMI 2.0) are given a Premium High Speed HDMI cable certification.

Cables that have been tested at an ATC to reliably handle signals up to 12.0 GHz per channel on 4 channels (48.0 Gbit/s aggregate, or maximum speed of HDMI 2.1) are given a Ultra High Speed HDMI cable certification.

Please note that version numbers are not a proper or officially recognized way of describing cables, so "HDMI 2.1 cable" has no official meaning and does NOT mean the cable has been certified at an authorized testing center. In fact advertising version numbers on cables has been explicitly banned by the HDMI Licensing Authority and any such cables are automatically considered non-compliant. Genuine certified cables have a special logo which you can read more about on the HDMI website. There are many cables which have not passed certification, and they will advertise terms like "4K certified" or "HDMI 2.0 certified" or whatever, rather than the real title which is "Premium High Speed HDMI cable" and so forth. So watch out for those. Always look for the certification logo.

Anyway, as for the original question... Will a premium cable outperform a standard cable, if they have both passed the same certification? Well, it depends what you mean by "premium cable".

If you mean "a Premium High Speed certified HDMI cable", well if both cables have passed the certification, then they are both premium HDMI cables.

If you just meant "a really good quality HDMI cable vs. a normal quality HDMI cable", well again, if they have both passed the same certification. There will be no difference within the bounds of the certification. If two cables both passed the Premium High Speed HDMI cable certification, then that means they were both tested to reliably handle 18 Gbit/s speeds. If you use them at 18 Gbit/s or below, there will be no difference between them.

How the cables perform at speeds higher than that is a mystery, it's entirely possible that one cable just barely passes the certification, and will stop working at 25 Gbit/s, while the "high quality cable" will continue working up to 50 Gbit/s, you never know. So, you could make an argument for "future-proofing" by buying cables that can handle speeds way beyond what the specification demands today. But I don't think this is very wise, because:

1. There's no such thing as a "bandwidth meter" that a normal person can buy, so the only way to "check" is by having hardware that can operate at that speed
2. So, when you buy cables with "future proof extra bandwidth", you won't be able to check that it's true for many years (read: long after your warranty has expired)
3. Cable vendors have already demonstrated, they don't give a shit about outright lying about the speeds their cables can handle if customers don't have an easy way to check

For further reading, I would suggest this.

Got work to do, so there may be some minor mistakes above, I don't really have time to proofread right now :)

If the cables actually conform to the standards specified, then there will be no difference between a "premium" or "ordinary" cable, since the signals in question are digital.

However, in reality you may find cables that do not conform to the standard that are advertised otherwise.