Editing No-cloning theorem (section)

== Consequences ==
*The no-cloning theorem prevents the use of certain classical [[error correction]] techniques on quantum states. For example, backup copies of a state in the middle of a [[quantum computer|quantum computation]] cannot be created and used for correcting subsequent errors.  Error correction is vital for practical quantum computing, and for some time it was unclear whether or not it was possible. In 1995, [[Peter Shor|Shor]] and [[Andrew Steane|Steane]] showed that it is, by independently devising the first [[quantum error correction|quantum error correcting]] codes, which circumvent the no-cloning theorem.
*Similarly, cloning would violate the [[no-teleportation theorem]], which says that it is impossible to convert a quantum state into a sequence of classical bits (even an infinite sequence of bits), copy those bits to some new location, and recreate a copy of the original quantum state in the new location. This should not be confused with [[quantum teleportation|entanglement-assisted teleportation]], which does allow a quantum state to be destroyed in one location, and an exact copy to be recreated in another location.
* The no-cloning theorem is implied by the [[no-communication theorem]], which states that quantum entanglement cannot be used to transmit classical information (whether superluminally, or slower).  That is, cloning, together with entanglement, would allow such communication to occur.   To see this, consider the [[EPR paradox|EPR thought experiment]], and suppose 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 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 no cloning theorem prevents an interpretation of the [[holographic principle]] for [[black hole]]s as meaning that there are two copies of information, one lying at the [[event horizon]] and the other in the black hole interior. This leads to more radical interpretations, such as [[black hole complementarity]].