Simultaneous Quantum Transmission and Teleportation of Unknown Photons Using Intra- and Inter-particle Entanglement Controlled-NOT Gates via Cross-Kerr Nonlinearity and P-Homodyne Measurements

We propose an arbitrary controlled-unitary (CU) gate and a simultaneous quantum transmission and teleportation (SQTTP) scheme. The proposed CU gate utilizes photons with cross-Kerr nonlinearities (XKNLs), coherent superposition states (CSSs) and P-homodyne detectors and consists of the consecutive operation of a controlled-path (C-path) gate and a gathering-path (G-path) gate It is almost deterministic and feasible with current technology when strong CSSs and weak XKNLs are employed. Compared with the existing multi-qubit or controlled gates, which utilize XKNLs, coherent states, and X-homodyne detectors, the proposed CU gate can increase the feasibility of experimental realization, and enhance the robustness against the decoherence effect. Based on the CU gate, we present a SQTTP scheme that simultaneously transmits and teleports two unknown states of photons between two parties (Alice and Bob) using path-polarization intra-particle hybrid entanglement (IRHE) by transferring only a single photon. Consequently, it is possible to experimentally implement SQTTP with a certain success probability using the proposed CU gate.