Their probability distributions don't factorize and this has consequences thzt can be calculated and measured. The details are in any course and/or textboook on quantum mechanics.

More exactly, the wave function doesn't factorise into the tensor product of two wave functions, each in its own configuration space. This means that when a measurement is performed on a particle, the whole wave function collapse, which describes the other particle too. There is then a correlation between the measurements on both particle that can't be explained classically.

Opposite phases of quantum states are conserved by spacetime parity.