Optimal manipulations with qubits: Universal quantum entanglers

Abstract

We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|\Psi >$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|\Psi >|0>+|0>|\Psi >)$. 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 $F=(9+3\sqrt{2})/14\simeq 0.946$. We also analyze how to optimally generate from a single qubit initially prepared in an unknown state $|Ψ\r$ a two qubit entangled system which is as close as possible to a Bell state $(|\Psi \mathring{|}{\Psi }^{\perp }\mathring{+}|{\Psi }^{\perp }\mathring{|}\Psi \mathring{)}$, where $ł\Psi |{\Psi }^{\perp }\mathring{=}0$.

11 pages, 3 eps figures, accepted for publication in Phys. Rev. A

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