Disclaimer: I am not an expert, but I understood this stuff pretty well 5 years ago. If you have a single particle there is no local experiment that you can do

Disclaimer: I am not an expert, but I understood this stuff pretty well 5 years ago. If you have a single particle there is no local experiment that you can do to determine whether that is entangled to a particle somewhere else. You need to use both particles in the experiment in order to prove it one way or the other. Mathematically, this is due to the fact that the density function for one half of an entangled pair is the same as the maximally mixed state for one particle. See CHSH[1] for an example of an experiment you can do if you have access to both particles and you want to show they are entangled. [1] https://en.wikipedia.org/wiki/CHSH_inequality https://en.wikipedia.org/wiki/CHSH_inequality