Quantum-Cloning Valerio Scarani - Chapter Three

Context 1982 Wooters and Zurek Nature 1982 Dieks Asher Peres ph/pdf/0205/ v1.pdfhttp://arxiv.org/PS_cache/quant- ph/pdf/0205/ v1.pdf No classical error correction! (but Q Error Corr. possible, Shor) No classical teleportation! (but Q Teleportation possible, see next chapter) Imperfect Quantum Cloning

The Classical Copier Source + Blank → Source + Copy X + B → X + X Y + B → Y + Y … + B → … + … the outcome does not depend on B! The procedure is independent of the source: is the operation below a copier? D + B → D + D X + B → X + D Y + B → ? Is the copier affected by the act of copying X+B+C → B+B+C’ ?

Quantum Transformations How does one transform a Quantum State? | ψ> → | ψ’> 1.Evolution: affect it with dynamics Smooth (& probability preserving = ) e.g. Schroedinger equation (differential eqn.) 2.Measurement: ask a question to the system Sudden (& probability preserving) e.g. The measurement postulate (projective) 3.Can the two be reconciled?

No-Cloning Theorem Show using unitarity or conservation of probability |V>|B> =|VB> → |VV> |α >|B> =|αB > → |αα > Compare and Show using linearity (homework)

Imperfect Copying The copier that does not work at all is unitary! The copier that is unitary does not work! There must be an “optimal” copier Fidelity of cloning: did we get what we want? Trivial (random) cloning gives F=3/4 Optimal (Buzek-Hillery) cloning gives F= 5/6