Editing No-communication theorem (section)

== Some comments ==
* The no-communication theorem implies the [[no-cloning theorem]], which states that quantum states cannot be (perfectly) copied.  That is, cloning is a sufficient condition for the communication of classical information to occur.   To see this, suppose that quantum states could be cloned. Assume parts of a [[Maximally entangled state|maximally entangled]] [[Bell state]] are distributed to Alice and Bob. Alice could send bits to Bob in the following way: If Alice wishes to transmit a "0", she measures the spin of her electron in the '''z''' direction, collapsing Bob's state to either <math>|z+\rangle_B</math> or <math>|z-\rangle_B</math>.  To transmit "1", Alice does nothing to her [[qubit]]. Bob creates many copies of his electron's state, and measures the spin of each copy in the '''z''' direction. Bob will know that Alice has transmitted a "0" if all his measurements will produce the same result; otherwise, his measurements will have outcomes <math>|z+\rangle_B</math> or <math>|z-\rangle_B</math> with equal probability. This would allow Alice and Bob to communicate classical bits between each other (possibly across [[space-like]] separations, violating [[causality]]).
* The version of the no-communication theorem discussed in this article assumes that the quantum system shared by Alice and Bob is a composite system, i.e. that its underlying Hilbert space is a tensor product whose first factor describes the part of the system that Alice can interact with and whose second factor describes the part of the system that Bob can interact with. In [[quantum field theory]], this assumption can be replaced by the assumption that Alice and Bob are [[Spacetime#Space-like interval|spacelike separated]].<ref>{{citation |last1=Eberhard |first1=Phillippe H. |last2=Ross |first2=Ronald R.|title=Quantum field theory cannot provide faster than light communication |year= 1989 | journal=Foundations of Physics Letters | volume=2 | issue=2 |pages=127–149 | doi=10.1007/bf00696109|bibcode=1989FoPhL...2..127E |s2cid=123217211 |url=http://www.escholarship.org/uc/item/5604n7md }}</ref> This alternate version of the no-communication theorem shows that [[faster-than-light communication]] cannot be achieved using processes which obey the rules of quantum field theory.