Editing No-cloning theorem (section)

== Generalization ==

In the statement of the theorem, two assumptions were made: the state to be copied is a [[pure state]] and the proposed copier acts via unitary time evolution. These assumptions cause no loss of generality. If the state to be copied is a [[mixed state (physics)|mixed state]], it can be [[purification of quantum state|"purified]]," i.e. treated as a pure state of a larger system. Alternately, a different proof can be given that works directly with mixed states; in this case, the theorem is often known as the no-broadcast theorem.<ref>{{Cite journal|last1=Barnum|first1=Howard|last2=Caves|first2=Carlton M.|last3=Fuchs|first3=Christopher A.|last4=Jozsa|first4=Richard|last5=Schumacher|first5=Benjamin|date=1996-04-08|title=Noncommuting Mixed States Cannot Be Broadcast|journal=Physical Review Letters|volume=76|issue=15|pages=2818–2821|doi=10.1103/PhysRevLett.76.2818|pmid=10060796|arxiv=quant-ph/9511010|bibcode=1996PhRvL..76.2818B|s2cid=11724387}}</ref><ref>{{Cite journal|last1=Kalev|first1=Amir|last2=Hen|first2=Itay|date=2008-05-29|title=No-Broadcasting Theorem and Its Classical Counterpart|journal=Physical Review Letters|volume=100|issue=21|pages=210502|doi=10.1103/PhysRevLett.100.210502|pmid=18518590|arxiv=0704.1754|bibcode=2008PhRvL.100u0502K|s2cid=40349990}}</ref>  Similarly, an arbitrary [[quantum operation]] can be implemented via introducing an [[Ancilla bit|ancilla]] and performing a suitable unitary evolution.{{clarify|reason=What other quantum operations are there? The phrasing of the proof in the previous section contains the implicit claim that we had them all when we had unitary ones and Hermitian ones. Now there are more? These new operations should be spelled out. The linked article is a grab bag.|date=May 2015}}  Thus the no-cloning theorem holds in full generality.