Editing No-cloning theorem (section)

{{Short description|Theorem in quantum information science}}
{{quantum}}In [[physics]], the '''no-cloning theorem''' states that it is impossible to create an independent and identical copy of an arbitrary unknown [[quantum state]], a statement which has profound implications in the field of [[quantum computer|quantum computing]] among others. The theorem is an evolution of the 1970 [[no-go theorem]] authored by James Park,<ref name="park">{{cite journal
 | last1 = Park | first1 = James
 | year = 1970
 | title = The concept of transition in quantum mechanics
 | journal = [[Foundations of Physics]]
 | volume = 1 | issue = 1
 | pages = 23–33
 |doi = 10.1007/BF00708652 | bibcode = 1970FoPh....1...23P| citeseerx = 10.1.1.623.5267
 | s2cid = 55890485
 }}</ref> in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by [[William Wootters]] and  [[Wojciech H. Zurek]]<ref name="wootterszurek">{{cite journal
 | last1 = Wootters | first1 = William 
 | last2 = Zurek| first2 = Wojciech 
 | year = 1982
 | title = A Single Quantum Cannot be Cloned
 | journal = [[Nature (journal)|Nature]]
 | volume = 299 | issue = 5886 
 | pages = 802–803
 |bibcode = 1982Natur.299..802W |doi = 10.1038/299802a0 | s2cid = 4339227 
 }}</ref> as well as [[Dennis Dieks]]<ref name="dieks">{{cite journal
 | last = Dieks| first = Dennis
 | year = 1982
 | title = Communication by EPR devices
 | journal = [[Physics Letters A]]
 | volume = 92 | issue = 6 | pages = 271–272
 |bibcode = 1982PhLA...92..271D |doi = 10.1016/0375-9601(82)90084-6 | citeseerx = 10.1.1.654.7183
 | hdl = 1874/16932
 }}</ref> the same year). The aforementioned theorems do not preclude the state of one system becoming [[quantum entanglement|entangled]] with the state of another as cloning specifically refers to the creation of a [[separable state]] with identical factors. For example, one might use the [[controlled NOT gate]] and the [[Hadamard transform#Quantum computing applications|Walsh–Hadamard gate]] to entangle two [[qubit]]s without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. The no-cloning theorem (as generally understood) concerns only [[pure state]]s whereas the generalized statement regarding [[mixed state (physics)|mixed states]] is known as the [[no-broadcast theorem]]. The no-cloning theorem has a time-reversed [[dual (category theory)|dual]], the [[no-deleting theorem]].