No-cloning Theorem - Consequences

Consequences

• The no-cloning theorem prevents us from using classical error correction techniques on quantum states. For example, we cannot create backup copies of a state in the middle of a quantum computation, and use them to correct subsequent errors. Error correction is vital for practical quantum computing, and for some time this was thought to be a fatal limitation. In 1995, Shor and Steane revived the prospects of quantum computing by independently devising the first quantum error correcting codes, which circumvent the no-cloning theorem.

• Similarly, cloning would violate the no teleportation theorem, which says classical teleportation (not to be confused with entanglement-assisted teleportation) is impossible. In other words, quantum states cannot be measured reliably.

• The no-cloning theorem does not prevent superluminal communication via quantum entanglement, as cloning is a sufficient condition for such communication, but not a necessary one. Nevertheless, consider the EPR thought experiment, and suppose quantum states could be cloned. Assume parts of a 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 or . 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 +1/2 and −1/2 with equal probability. This would allow Alice and Bob to communicate across space-like separations.

• The no cloning theorem prevents us from viewing the holographic principle for black holes as meaning we have two copies of information lying at the event horizon and the black hole interior simultaneously. This leads us to more radical interpretations like black hole complementarity.