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Optimal manipulations with qubits: Universal quantum entanglers

Vladimir Buzek·Mark Hillery
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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 $|Ψ>$ 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 $(|Ψ>|0> +|0>|Ψ>)$. 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 $F= (9+3\sqrt{2})/14\simeq 0.946$. 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 $(|Ψ\r|Ψ^\perp\r+|Ψ^\perp\r|Ψ\r)$, where $łΨ|Ψ^\perp\r =0$.

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Vladimir Buzek, Mark Hillery. 2000-06-09. Optimal manipulations with qubits: Universal quantum entanglers. https://doi.org/10.1103/physreva.62.022303

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