# Quantum cloning

Quantum cloning is a 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:

${\displaystyle U|\psi \rangle _{A}|e\rangle _{B}=|\psi \rangle _{A}|\psi \rangle _{B}}$,

where ${\displaystyle U}$ is the actual cloning operation, ${\displaystyle |\psi \rangle _{A}}$ is the state to be cloned, and ${\displaystyle |e\rangle _{B}}$ 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 states that there is no operation for cloning any arbitrary state ${\displaystyle |\psi \rangle _{A}}$. Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit fidelity. A universal cloning machine can have a fidelity as high as 5/6.[1]

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[who?] 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.[2] Ion trapping techniques have been applied to cloning quantum states of ions.[3]

It may be possible to clone a quantum state to arbitrary accuracy in the presence of closed timelike curves.[4]

## References

1. ^ Bužek V. and Hillery, M. Quantum Copying: Beyond the No-Cloning Theorem. Phys. Rev. A 54, 1844 (1996)
2. ^ Antía Lamas-Linares, Christoph Simon, John C. Howell, Dik Bouwmeester, Experimental Quantum Cloning of Single Photons, Science 296 5568 (2002)
3. ^ YANG, Rong-Can; LI, Hong-Cai†; LIN, Xiu; HUANG, Zhi-Ping; XIE, Hong (Jan 2008). "Implementing a Universal Quantum Cloning Machine via Adiabatic Evolution in Ion-Trap System". Bibcode:2008CoTPh..49...80Y. doi:10.1088/0253-6102/49/1/17.
4. ^ Todd A. Brun, Mark M. Wilde, Andreas Winter, Quantum state cloning using Deutschian closed timelike curve. Physical Review Letters 111, 190401 (2013); arXiv:1306.1795