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Entangling photons via the quantum Zeno effect

The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate $ξ_{2γ}$ exceeds the one-photon loss rate $ξ_{1γ}$. In order to reach an error probability $P_{\rm error}$, we need $ξ_{1γ}/ξ_{2γ}<2P_{\rm error}^2/π^2$, which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have $ξ_{2γ}<ξ_{1γ}$, we discuss three mechanisms for enhancing two-photon absorption as compared to one-photon loss. The first mechanism again employs the quantum Zeno effect via self-interference effects when sending two photons repeatedly through the same absorber. The second mechanism is based on coherent excitations of many atoms and exploits the fact that $ξ_{2γ}$ scales with the number of excitations but $ξ_{1γ}$ does not. The third mechanism envisages three-level systems where the middle level is meta-stable ($Λ$-system). In this case, $ξ_{1γ}$ is more strongly reduced than $ξ_{2γ}$ and thus it should be possible to achieve $ξ_{2γ}/ξ_{1γ}\gg1$. In conclusion, although our scheme poses challenges regarding the density of active atoms/molecules in the absorber medium, their coupling constants and the detuning, etc., we find that a two-photon gate with an error probability $P_{\rm error}$ below 25% might be feasible using present-day technology.