Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity<xref ref-type="fn" rid="cpb141732fn1">*</xref>

Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity*

Heo Jino^a),^b), Hong Chang-Ho^a),^b), Lim Jong-In^a),^b), Yang Hyung-Jin^a),^c)†

(a) Alice’s side in Fig. 3 , when the CU (CZ, CNOT) operations are performed between the control photon T (the transmission photon) and the target photon A (Alice’s unknown state | ψ 〉_A). (b) Schematic illustration of the CU gate, in which the C-path and G-path gates are consecutively performed by XKNLs, X-homodyne detectors, and feed-forwards, as described in Section 2. If the unitary operator U in the middle between the C-path and G-path gates is σ_Z or σ_X , then the CU gate will become a CZ gate or a CNOT gate. The PBS in front of the C-path gate and the PBS at the rear of the G-path gate in path P–Q refer to the split-path of control photon T. The details are presented in Appendix A. (c) A detailed description of the operations on Alice’s side, using a CZ gate and CNOT gate (the consecutive operation of a C-path gate and a G-path gate) via XKNLs, X-homodyne detectors, and feed-forwards.