Optimal manipulations with qubits: Universal quantum entanglers

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Abstract
We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler that entangles a qubit in unknown state |Ψ〉 with a qubit in a reference (known) state |0〉. That is, our entangler generates the output state that is as close as possible to the pure (symmetrized) state (|Ψ〉|0〉+|0〉|Ψ〉). The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e., the distance between the output and the ideally entangled—symmetrized state) does not depend on the input and takes the constant value F=(9+32)/14≃0.946. We also analyze how to optimally generate from a single qubit initially prepared in an unknown state |Ψ〉 a two qubit entangled system, which is as close as possible to a Bell state (|Ψ〉|Ψ⊥〉+|Ψ⊥〉|Ψ〉), where 〈Ψ|Ψ⊥〉=0.
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