I have a digital camera with HDMI output and I want to use it as a high quality “webcam.” I am looking for a device which takes a 1080p/60fps HDMI video signal as input and outputs that signal over USB for usage on a computer as if it were a webcam. It will need to be compatible with USB 3.0 or greater to accommodate the necessary bandwidth.
I suspect what you will need here is a 'virtual webcam' - i.e. it's not just a media (socket) converter you need here, but a 'box' which the computer, via USB, detects as a webcam.
Consider a normal webcam - it contains a small camera and a set of circuits which get that video from the camera to the computer. The computer recognises these circuits as 'a webcam' and, via appropriate drivers, then knows what to do with it.
What you are looking for is for your digital camera to act as a Webcam. Unless it has this functionality built in (in which case it would have some sort of USB interface and appropriate software/drivers to suit) then you need the actual 'webcam' (set of circuits I described above) to sit in between your camera and your computer.
So, effectively, what you need is a 'webcam' (set of circuits) which instead of taking its picture from a small, on-board camera, takes its picture from an HDMI input socket. The rest of the circuitry, after that point, would be the same as any standard webcam - and the computer would see it as a webcam.
This type of functionality may be more likely to exist as some sort of USB video capture card, rather than an HDMI to USB converter, as most 'HDMI to USB' adapters will be intended for output rather than input - i.e. connecting an external HDMI monitor to a computer by USB.
If such a device exists, I suspect it will cost more than a decent HD webcam. Unless the camera you want to use is 'professional grade', i.e. priced at thousands of pounds/dollars, I suspect you will be better off with a decent, modern webcam. I've personal experience with the Logitech series - we use several models in the £50-£200 mark in our offices for video conferencing. They also do wide angle models if required.
As of 2021 (five years after I asked this original question), the best product for this is the Elgato Cam Link 4K. If you find it on sale, it can be had for around $100.