Faithful Entanglement Swapping Based on Sum-Frequency Generation

We show that an entanglement swapping operation performed with spontaneous parametric down-conversion can be made faithful without postselection using sum-frequency generation. This invites us to revisit the sum-frequency process and from a proof-of-principle experiment, we demonstrate that it provides a realistic solution for nonlinear optics at the single-photon level. This opens the way to attractive alternatives to six-photon protocols based on linear optics used, e.g., for the heralded creation of maximally entangled pairs or for device-independent quantum key distribution.

Figure 1

Basic scheme for entanglement swapping. Sources (stars) produce entangled pairs, $A\mathrm{\text{−}}B$ and $C\mathrm{\text{−}}D$. The projection of $B$ and $C$ in the Bell basis entangles the photons $A$ and D.

Figure 2

Proposed setup for faithful entanglement swapping. The Bell measurement is based on SFG followed by an interferometer (made with one optical switch and one beam splitter) to erase the which-path information; cf. text for details.

Figure 3

Proposed setup to overcome the problem of transmission losses in DI-QKD. Each Alice and Bob boxes includes a measurement apparatus allowing them to choose a measurement ($X$ and $Y$, respectively) and to obtain outputs ($a$ and $b$). If the resulting probability distribution $P(ab|XY)$ violates the CHSH inequality by a sufficient amount, a key can distill from the remaining data. Since Bob inputs a $Y$ only when a SFG photon is detected, Alice and Bob can safely discard all events where a photon is lost during the transmission.

Figure 4

Probability ${\eta }_{\mathrm{SFG}}$ that a signal photon ($\lambda =1563\mathrm{nm}$, $\Delta \lambda =0.3\mathrm{nm}$) is upconverted when interacting with a weak pump ($\lambda =1557\mathrm{nm}$, $\Delta \lambda =1.2\mathrm{nm}$) inside the waveguide, plotted against the number of photons per mode (equal for pump and signal). Experimentally pump and signal photons are obtained by attenuating and filtering a light-emitting diode. Upconverted photons are separated from the residual pump using a prism, they are then detected with a single photon detector (IDQ ID100, 6% efficiency). Dark counts (2.2 Hz) have been subtracted, and injection (3 dB), reflection (0.6 dB), and propagation (0.2 dB) losses have been taken into account.