The paper unifies state and channel cloning, proves that a channel family can super-replicate only when a certain generator β(x) is nonzero, and exhibits noisy phase gates as the first non-unitary examples.
Optimal universal quantum cloning and state estimation
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abstract
We derive a tight upper bound for the fidelity of a universal N to M qubit cloner, valid for any M \geq N, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalise the operation of a quantum cloner to mixed and/or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind.
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Cloning Quantum Channels
The paper unifies state and channel cloning, proves that a channel family can super-replicate only when a certain generator β(x) is nonzero, and exhibits noisy phase gates as the first non-unitary examples.