Quantum cloning
Encyclopedia
Quantum cloning is the process that takes an arbitrary, unknown quantum state and makes an exact copy without altering the original state in any way. In Dirac notation, the process of quantum cloning is described by:
,
where
is the actual cloning operation, 
is the state to be cloned, and 
is the initial state of the copy.
Quantum cloning is forbidden by the laws of quantum mechanics
as shown by the no cloning theorem
, which proves that there is no
that can perform the cloning operation for any arbitrary state 
. Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit fidelity
with the state being cloned.
The quantum cloning operation is the best way to make copies of quantum information therefore cloning is an important task in quantum information processing, especially in the context of quantum cryptography. Researchers are seeking ways to build quantum cloning machines, which work at the so called quantum limit. The first cloning machine relied on stimulated emission to copy quantum information encoded into single photons. Teleportation, nuclear magnetic resonance, quantum amplification and superior phase conjugation have been some other methods utilized to realize a quantum cloning machine.
,where
is the actual cloning operation, is the state to be cloned, and is the initial state of the copy.Quantum cloning is forbidden by the laws of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
as shown by the no cloning theorem
No cloning theorem
The no-cloning theorem is a result of quantum mechanics that forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.The state of one system can be...
, which proves that there is no
that can perform the cloning operation for any arbitrary state . Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit fidelityFidelity of quantum states
In quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space.- Motivation :...
with the state being cloned.
The quantum cloning operation is the best way to make copies of quantum information therefore cloning is an important task in quantum information processing, especially in the context of quantum cryptography. Researchers are seeking ways to build quantum cloning machines, which work at the so called quantum limit. The first cloning machine relied on stimulated emission to copy quantum information encoded into single photons. Teleportation, nuclear magnetic resonance, quantum amplification and superior phase conjugation have been some other methods utilized to realize a quantum cloning machine.