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Quantum-Cloning

Quantum-Cloning. Valerio Scarani - Chapter Three. Context. 1982 Wooters and Zurek Nature 1982 Dieks Asher Peres http:// arxiv.org/PS_cache/quant-ph/pdf/0205/0205076v1.pdf No classical error correction! ( but Q Error Corr. possible, Shor )

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Quantum-Cloning

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  1. Quantum-Cloning Valerio Scarani - Chapter Three

  2. Context • 1982 Wooters and Zurek Nature • 1982 Dieks • Asher Peres http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205076v1.pdf • No classical error correction! (butQ Error Corr. possible, Shor) • No classical teleportation! (but Q Teleportation possible, see next chapter) • Imperfect Quantum Cloning

  3. 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’ ?

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

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

  6. 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

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