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) Bob’s side in Fig. 3 , when the CU (CY, CNOT) operations are performed between the control photon T (the transmission photon) and the target photon B (Bob’s unknown state | φ 〉_B). (b) Schematic depiction of the CU gate, in which the C-path gate and the G-path gate 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 gate and the G-path gate is i σ_Y or σ_X , then the CU gate becomes a CY gate or CNOT gate. Furthermore, the PBSs in front of the C-path gate and at the rear of the G-path gate in the paths P₁–P₂ and Q₁–Q₂ refer to the split-path of the control photon T. The details are presented in Appendix B. (c) Detailed description of the operations on Bob’s side, using a CY gate and CNOT gate (the consecutive operation of C-path gate and G-path gate) via XKNLs, X-homodyne detectors, and feed-forwards.