Resource-efficient linear-optical quantum router

An all-linear-optical scheme for a fully featured quantum router is presented. This device directs the signal photonic qubit according to the state of one control photonic qubit. In the introduction we formulate the list of requirements imposed on a fully quantum router. Then we describe our proposal, showing the exact principle of operation on a linear-optical scheme. Subsequently we provide a generalization of the scheme in order to optimize the success probability by means of a tunable controlled-phase gate. Finally, we show how one can modify the device to route multiple signal qubits using the same control qubit.

Figure 1

Conceptual scheme of a quantum router.

Figure 2

Scheme of the linear-optical implementation of a quantum router. PBS denotes polarizing beam splitter, PDBS denotes polarization dependent beam splitter, $\lambda /2$ and $\lambda /4$ denote half- and quarter-wave plates, NDF denotes neutral-density filter, c-phase denotes controlled phase gate, QND denotes quantum nondemolition detector, PPG denotes programmable-phase gate, and D/A denotes polarization analysis (for more details see Ref. [27]). Red lines depict signal modes, while blue lines depict control modes.

Figure 3

Success probability of the routing procedure as a function of the routing ratio parameter $\chi$. Additionally the plot shows the relation between the routing parameter $\chi$ and the control qubit parameter $\theta$.

Figure 4

(a) Linear-optical scheme of a tunable c-phase gate. The interaction Mach-Zehnder interferometer replaces the fixed polarization dependent beam splitter (PDBS) in the original scheme. The phase shift imposed by the gate is tuned by setting specific values of phase shift (PS) and losses (NDF) in this interferometer (for more details see Ref. [31]). (b) Modified scheme of the router using two tunable c-phase gates. Red lines depict signal modes, while blue lines depict control modes.

Figure 5

Maximum and minimum success probability of the router using two tunable c-phase gates depicted as functions of the routing ratio limit. The plot indicates that for sufficiently small values of routing ratio limit the tunable c-phase gate offers better performance than the scheme devised in the previous section (maximum and minimum success probability of the previous scheme is depicted using black dashed lines at $\frac{1}{8}$ and $\frac{1}{24}$). The dotted line shows the success probability if the standard state-independent c-phase gate is used instead of the generalized version.

Figure 6

Scheme for multiqubit routing; $c$ denotes the classical optical coupler. Red lines depict signal modes, while blue lines depict control modes.