Figure 1

(Color online) Structure of QND module. (a) The interaction of one of the coherent beams $|{\alpha }_0⟩$ with a single-photon state in Kerr medium generates an extra phase $\theta$ on the coherent beam. A 50-50 beam splitter (the one on the right) transforms the coherent-state product ${|{\alpha }_0⟩}_1{|{\beta }_0⟩}_2$, where ${|{\beta }_0⟩}_2={|{\alpha }_0⟩}_2$ or ${|{\alpha }_0{e}^{i\theta }⟩}_2$, to ${|\frac{{\alpha }_0-{\beta }_0}{\sqrt{2}}⟩}_1{|\frac{{\alpha }_0+{\beta }_0}{\sqrt{2}}⟩}_2$. A response of the photodiode D indicates that the two beams ${|{\alpha }_0⟩}_1$ and ${|{\beta }_0⟩}_2$ are different with ${|\frac{{\alpha }_0-{\beta }_0}{\sqrt{2}}⟩}_1\ne {|0⟩}_1$. (b) Inside the Kerr medium, the single photon and the coherent beam with the different polarizations are transmitted together.Reuse & Permissions

Figure 2

(Color online) Layout of setup for generating the elementary links. By two linear optical circuits A and B, each component $|{\Lambda }_i⟩$ of a photon pair state in Eq. (3), which is sent to A1-B1 terminals, is transformed to a superposition, ${|{\Sigma }_i⟩}_{K_A,K_B}+{|{\Sigma }_i⟩}_{K_A,R_B}+{|{\Sigma }_i⟩}_{R_A,K_B}+{|{\Sigma }_i⟩}_{R_A,R_B}$, over four pairs of output ports. Each of these states is a fixed linear combination of two Bell states (one even parity but the other odd). Through the Kerr media, two coherent pulse trains running between the output ports interact with the single photons at location A and B in the order specified here (the first coherent state is coupled to $H$ mode and the second to $V$ mode at location B, and they are coupled to the photons at location A in the opposite way), and separate the even and the odd parity components of the photon pairs. The detection of a local QND module heralds the single-photon modes to be coupled to the traveling coherent beams and mapped to quantum memory. Upon receiving a successful result of the $M$ module and the measurement result of the QND module from location A, which are transmitted through a classical communication channel, the system operator at location B determines the generation and the type of an elementary link between A2-B2 terminals, together with the measurement of his/her local QND module.Reuse & Permissions

Figure 3

The relation between $P_g$, the probability by a single try of entangling a photon pair, and $F$, the fidelity of the entangled pair. The distances between the repeater stations are chosen as 15, 27, 50, 75, and 100 km.Reuse & Permissions

Figure 4

The average times for distributing an entangled pair with some different coherent pulse repetition rates and connection probabilities. Here we assume $L_0=75\text{km}$, $P_g=5\times {10}^{-5}$, and $c=2\times {10}^5\text{km}/\text{s}$ in optical fiber, and neglect the time for local Bell-state measurements. By the connection strategy we present, $T_{tot}$ scales linearly if $P_c\ge 0.5$ and gets close to the two-way classical communication time with the also increased pulse train repetition rate $f$. The classical communication line is for comparison.Reuse & Permissions

Figure 5

The linear optical circuit that converts the input in polarization space to which-path space and implements $U_1$ of Eq. (A3). The state of a single photon is converted to a which-path space by PBS. Then the mirrors M and the 50-50 beam splitters transform the two-dimensional single-photon state to a four-dimension one. It is a part of the integrated circuits A or B in Fig. 2.Reuse & Permissions