Purification of Single-Photon Entanglement

Single-photon entanglement is a simple form of entanglement that exists between two spatial modes sharing a single photon. Despite its elementary form, it provides a resource as useful as polarization-entangled photons and it can be used for quantum teleportation and entanglement swapping operations. Here, we report the first experiment where single-photon entanglement is purified with a simple linear-optics based protocol. In addition to its conceptual interest, this result might find applications in long distance quantum communication based on quantum repeaters.

Figure 1

Scheme for entanglement purification of single-photon entanglement. Alice and Bob share two entangled single-photon states ${\rho }_{a_1{b}_1}$, ${\rho }_{a_2{b}_2}$ [of the form given in Eq. (1)] with fidelity $F_1$ and $F_2$, respectively. While Alice combines the modes $a_1$ and $a_2$ on a $15/85$ beam splitter, Bob couples the modes $b_1$ and $b_2$ on a $85/15$ beam splitter. The detection of one photon in either $d_a$ or $d_b$ projects the modes $\tilde{a}$ and $\tilde{b}$ into a single-photon entangled state ${\rho }_{\tilde{a}\tilde{b}}$ with higher fidelity $\tilde{F}$.

Figure 2

Experimental setup. Pairs of orthogonally polarized photons are created by a waveguide-based source, separated by a PBS and coupled into optical fibers. Each photon passes through a $50/50$ coupler (BS1 and BS2) to create two-mode entangled states ${\rho }_{a_1{b}_1}$ and ${\rho }_{a_2{b}_2}$. Alice and Bob each receive two modes, one from each state, and combine them using $15/85$ couplers (BS4 and BS5). Conditional on the detection of one photon by either Alice or Bob, a purified single-photon entangled state ${\rho }_{\tilde{a}\tilde{b}}$ is created. The degree of entanglement is measured using the $50/50$ coupler BS3. Two noise generators (${\varphi }_1$ and ${\varphi }_2$) are used to reduce the fidelities $F_1$ and $F_2$ of ${\rho }_{a_1{b}_1}$ and ${\rho }_{a_2{b}_2}$, respectively. The phase $\Phi$ is scanned using a piezo to acquire an interferogram and thus estimate the fidelities.

Figure 3

Raw interference fringes observed while the phase $\Phi$ is being scanned. (a) Coincidences between detectors $D_1$ (herald) and $D_4$ corresponding to the state ${\rho }_{a_2{b}_2}$. Initially, the fidelity is $F_2=(97.7\pm 0.2)\%$. When the noise generator ${\varphi }_2$ is switched on, the fidelity decreases to $F_2=(75.0\pm 0.7)\%$. (b) Coincidences between detectors $D_3$ and $D_4$ corresponding to the purified state ${\rho }_{\tilde{a}\tilde{b}}$. While both noise generators are on, the fidelity is $\tilde{F}=(79.6\pm 1.1)\%$. These values are obtained after the subtraction of accidental coincidences due to dark counts. Even when they are not subtracted, a definite purification effect can still be observed. The vertical lines mark every time the voltage ramp reaches its end, reversing the scan direction.

Figure 4

Distribution of the fidelity measurements. Probability densities P as a function of the measured fidelities for (a) state ${\rho }_{a_1{b}_1}$, (b) state ${\rho }_{a_2{b}_2}$ and (c) the purified state ${\rho }_{\tilde{a}\tilde{b}}$. The corresponding mean fidelity and standard deviation are given next to each distribution. The curves are Gaussian functions with the same mean and $\sigma$ as the sample data. The number of bins chosen is the optimal one using Scott’s principle [22]. The agreement with the histogram can be seen by the fact that the fitted curve passes through the center of most histogram bars.