The no-cloning theorem shows that we can't build a unitary machine which will make a perfect...

 

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The no-cloning theorem shows that we can't build a unitary machine which will make a perfect copy of an unknown quantum state. But if we are willing to settle for an "imperfect" copy, what fidelity might we achieve? Consider a machine that acts on 3-qubit states according to |000) ABC V J00) AB |0)c + lebt)AB|1)c |100) ABC V |11) AB |1)c + Test) aB |0)c a) Is such a device physically realizable, in principle? If the machine operates on the initial state |)A |00) BC; it produces an pure entangled state |b) ABC of the three qubites. But if we observe qubit A alone, its final state is the density operator pa Similarly, the qubit B, observed in isolation, has the final state pg. It is easy to see that pa = PB - these are identical but imperfect copies of the input pure state |)A- c) For |)A = a|0) A + b[1)A, find p'a, and compute its fidelity F =A (lP'alb)A- tr Bc () ABC АВС (). The no-cloning theorem shows that we can't build a unitary machine which will make a perfect copy of an unknown quantum state. But if we are willing to settle for an "imperfect" copy, what fidelity might we achieve? Consider a machine that acts on 3-qubit states according to |000) ABC V J00) AB |0)c + lebt)AB|1)c |100) ABC V |11) AB |1)c + Test) aB |0)c a) Is such a device physically realizable, in principle? If the machine operates on the initial state |)A |00) BC; it produces an pure entangled state |b) ABC of the three qubites. But if we observe qubit A alone, its final state is the density operator pa Similarly, the qubit B, observed in isolation, has the final state pg. It is easy to see that pa = PB - these are identical but imperfect copies of the input pure state |)A- c) For |)A = a|0) A + b[1)A, find p'a, and compute its fidelity F =A (lP'alb)A- tr Bc () ABC АВС ().

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Fundamentally the nocloning theorem protects the uncertainty principle in quantum mechanics If one could clone an unknown state then one could make as many copies of it as one wished and measure each ... View the full answer