Technically, the microscopic causality postulate of axiomatic quantum field theory implies the impossibility of superluminal communication using any phenomena whose behavior can be described by orthodox quantum field theory. However, it is now well understood that quantum entanglement does not allow any influence or information to propagate superluminally. The impossibility of superluminal communication led Einstein, Podolsky, and Rosen to propose that quantum mechanics must be incomplete (see EPR paradox).
Entangled states lead to correlations in the results of otherwise random measurements, even when the measurements are made nearly simultaneously and at far distant points. Quantum mechanics is non-local in the sense that distant systems can be entangled. However, such fields have luminal signal velocity and do not allow superluminal communication. By contrast, tachyonic fields – quantum fields with imaginary mass – certainly do exist and exhibit superluminal group velocity under some circumstances.
These would allow superluminal communication, and for this reason are widely believed not to exist. Tachyonic particles are hypothetical particles that travel faster than light.
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