Using quantum routers to implement quantum message authentication and Bell-state manipulation

In this paper we investigate the capability of quantum routing (quantum state fusion) to implement two useful quantum communications protocols. The analyzed protocols include quantum authentication of quantum messages and nondestructive linear-optical Bell-state manipulation. We also present the concept of quantum decoupler—a device implementing an inverse operation to quantum routing. We demonstrate that both quantum router and decoupler can work as specialized disentangling gates.

Figure 1

Conceptual scheme of a quantum router as described in the text. Signal qubit $|{\psi }_s\rangle$ is routed into a coherent superposition of two output modes depending on the state of the control qubit $|{\psi }_c\rangle$.

Figure 2

Conceptual scheme of a quantum decoupler—a device inverse to a quantum router. There are two qubits stored in the signal photon. The first qubit is encoded in its spatial degree of freedom and the second in polarization. Quantum decoupler facilitates interaction between this signal input state and an ancillary qubit leading to transcription of the spatial mode encoded qubit to the state of the ancillary qubit while the second signal qubit remains stored in the signal state.

Figure 3

Scheme for polarization—spatial encoding swap: PBS, fully polarizing beam splitter (transmitting horizontal polarization and reflecting vertial polarization); HWP, half-wave plate (rotated by ${45}^{\circ }$ with respect to horizontal polarization).

Figure 4

The average transmission fidelity $F_{n,d}$ given by Eq. (14) for undetected individual counterfeiting of $n$-qubit long messages extended by $d$ decoy qubits. The fidelity is averaged over all possible cases of successful counterfeiting of extended message which includes attacks on 1 to $n+d$ qubits.

Figure 5

Same as in Fig. 4 but for the average counterfeiting probability $P_{n,d}$ given by Eq. (16).

Figure 6

Router assisted Bell-state discriminator as described in the text: PBS1, polarizing beam splitter transmitting horizontal and reflecting vertical polarization; PBS2 and PBS3, beam splitters transmitting diagonal and reflecting antidiagonal linear polarizations; DET, detection block with four detector each projecting onto one of the four Bell states.

Figure 7

Bell-state manipulation using quantum router. The two-qubit state is processed by a quantum router. One of the qubits acts as signal, the other as control. Subsequently, the output signal is split on Bell-state splitter depicted in Fig. 6. Set of four neutral density filters and phase shifters is used to adjust amplitude and phase of each individual Bell state separately. The signal is recombined on an inverse Bell-state splitter and finally two separate photons are recreated using the quantum decoupler described in Fig. 2.