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Cloning the Quantum

Writer's picture: Mishkat BhattacharyaMishkat Bhattacharya

Cloning in Biology


Cloning in the life sciences is a fascinating and controversial topic. Dolly the sheep was the first mammal to be cloned and CC the first pet (it was a cat). Currently, a large number of countries only allow therapeutic cloning - the production of stem cells used for understanding and treating disease.


Human cloning is forbidden and has never been carried out as far as we know. Concerns about cloning of live organisms include susceptibility to defects in organs and the immune system, premature aging, diminution of diversity in the gene pool, etc.


Cloning in Quantum Physics


In this context, it is also fascinating to note that in physics, a famous theorem forbids cloning of a quantum state. This is the No-Cloning Theorem, which takes only a few lines of linear algebra to prove, and which says that one cannot produce exact copies of an arbitrary quantum state.


Practical Implications


One of the important consequences of the No-Cloning Theorem is that it prevents the redundancy-based correction of errors in a quantum computer. In classical computers we can make multiple copies of a bit and take a majority vote if we think one or more of them have become corrupted (say one bit has flipped its value). This works to correct errors nicely as long as the probability of errors happening is small - usually the case - so the majority of the bits do not change from their fiducial value.


In a quantum computer redundancy cannot be used in this naive way as the No-Cloning Theorem does not allow us to copy the (quantum) information.


Peter Shor found a way around this problem, and thus made quantum computation realistic, by implementing redundancy using a resource from quantum mechanics called entanglement. Entanglement is the existence of correlations - that cannot be explained classically - between two or more objects.


In quantum error correction, the information in a single qubit (the quantum analog of the bit) is shared in a highly entangled state of 9 (some ancillary) qubits. This sophisticated enactment of redundancy allows for a tolerable fidelity of transmission of quantum information through a noisy channel.


Giving up Perfection


Interestingly, physics does allow for the imperfect cloning of a quantum state. In a pioneering paper, Buzek and Hillery came up with the design of a Universal (i.e. input-state-independent) Quantum Copying Machine (UQCM) which they showed could copy quantum states with a maximum fidelity of 5/6. Quite close to unity!


Imperfect cloning is nowadays used to simulate eavesdropping on quantum cryptography networks.


Two bonus remarks


i) A short proof of the No-Cloning Theorem: Heisenberg's uncertainty principle says that the position and momentum of a state cannot be determined precisely at the same time. But if we could clone the state, one copy could be used to measure the position exactly and the other the momentum. This would violate the uncertainty principle, and hence cannot be possible. (I find this proof a bit slick).


ii) It can be shown that if perfect quantum cloning is allowed then signals can be sent faster than light between two objects. In fact 'superluminal signaling' occurs for any fidelity of cloning greater than 5/6! This bound on cloning fidelity maintains peace between quantum physics and relativity [1].


[1] N. Gisin, Quantum cloning without signaling, Physics Letters A 242, 1 (1998).


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