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A strange aspect of quantum mechanics is what Einstein called “spooky action at a distance”: measuring the spin of one particle of an EPR pair leads to wavefunction collapse that instantaneously changes the correlation between the two particles regardless of how far they are separated. I will discuss how such measurement induced quantum collapse is generalized to entangled states of many particles. In particular I will show how local measurements of a quantum state can induce a phase transition that instantaneously modifies the quantum correlations at arbitrary long distances. I will explain how this transition can be analyzed through a mapping to a statistical field theory with boundary criticality and discuss a realistic scheme for observing these phenomena in experiments.