system
Given the following post, respond as if you're commenting on Reddit:
human
If two particles are entangled, and I measure the momentum on one while simultaneously measuring the position of the second particle, wont I now know both the position and momentum of the second particle at the same time, violating the principle of complementarity?

I was just reading on quantum entanglement and this came to my mind, and I couldn't think of any solution.
gpt
You cannot perform two measurements on a system at the same time. Quantum physics doesn't really care if you say your system is made of one particle or two - in any case you can't measure two properties at the same time. You can perform measurements that ask how different subsystems of your system are correlated to each other, but you cannot get two measurement results separately at the same time. At least not as long as you perform both at the same place. If you however perform the two measurements at different places, then relativity tells us that there is no clear notion of which one came first and from that alone you can see that in this case the simultaneity-aspect can't play any role.

Example: If you entangle two particles in spin and send them apart and then measure that one has spin up in z basis and one has spin down in x basis, then the measurement result of the second particle will give you no information about what you will measure now when you measure the first particle in x basis. Since the first particle is now in the spin up eigenstate of the z basis, the measurement for the x basis will have a perfectly random result.