It is being used to develop a quantum compass – an instrument that will exploit the behaviour of subatomic matter in order to develop devices that can accurately pinpoint their locations no matter where they are placed,

[...]

The aim of the Imperial College project [...] is to create a device that is not only accurate in fixing its position, but also does not rely on receiving external signals.

These statements imply the device can know exactly where it is in space just by measuring some purely internal quantum effect, which conflicts with the principles of Lorentz invariance and relativity.

Both are constructed around the same idea that there's nothing special in the laws of physics that changes with where you are or how fast you're going. That observation is what led the conclusion that the speed of light is the same in every reference frame, and to Einstein developing the theory of relativity.

In reality, the device needs an external signal to learn its initial position. And it's unlikely to be perfectly accurate so it may still need periodic updates, just hopefully a lot less frequently.

The London Underground is actually kind of a dumb use-case because it's fixed infrastructure. You can just have something like RFID tags around the track that the train reads as it goes by. And there's going to be sensors in the track that report trains' presence to a central control room. It's just a good setting to test the device.

What it's really potentially quite useful for is nuclear submarines since they can stay underwater pretty much as long as their food supplies last, and knowing their position without using sonar or being able to receive GPS signals is quite important for navigation and obstacle avoidance. But the author was probably told to downplay potential military applications.

You can’t use it to determine both your location and velocity at the same time. (/s)