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Quantum entanglement, simply put, is a correspondence between particles or systems of particles such that taking a measurement of one will predict the outcome of a similar measurement of the other.

The Heisenberg Uncertainty Principle states that there are variables associated with particles or systems of particles such that certain knowledge of one variable precludes the same degree of knowledge of the other - if you know the spin of a particle along the Z axis, you can't then know the spin of that same particle along the X axis.

What I was wondering is this - given a pair of entangled particles, measuring an arbitrary variable "A" on particle number 1 sets the value for that variable on particle number 2...so what happens when you then attempt to measure variable "B" on particle number 2 when variables "A" and "B" are incompatible observables? What result would such a measurement produce?