Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity*
Heo Jinoa),b), Hong Chang-Hoa),b), Lim Jong-Ina),b), Yang Hyung-Jina),c)†
       
Schematic diagram of the BQTP scheme between Alice and Bob using intra-particle hybrid entanglement and CU gates: Alice wants to teleport an unknown state | ψ 〉A of photon A to Bob, and Bob wants to teleport an unknown state | φ 〉B of photon B to Alice. To implement our simultaneous teleportation scheme, Alice prepares the transmission photon | H 〉T and generates photon T to the path-polarization intra-particle hybrid entangled state using a BS and an SF. After performing a CZ and a CNOT gate between the two photons T and A (| ψ 〉A), Alice transfers photon T to Bob. Subsequently, Bob performs a CY and CNOT gate between the two photons T and B for the teleportation of his unknown photon state | φ 〉B to Alice. Consequently, Alice and Bob can simultaneously teleport the unknown states | ψ 〉A and | φ 〉B to each other through BSs, PBSs, SFs, WPs, and CU operations (Alice’s side: a CZ gate and a CNOT gate, Bob’s side: a CY gate and CNOT gate). Then, Bob measures the path and polarization of the transmitted photon T through P-Ds (01-04). These measurement results and the information on the initial path of photon T are shared through a classical channel in order to reconstruct the teleported states of photons to obtain the initial unknown photon states, | ψ 〉A and | φ 〉B, by applying the appropriate unitary operators U A and U B . Consequently, Alice and Bob achieve simultaneous teleportation by transmitting only a single photon T, in which the states of photons A and B are converted to the unknown states | φ 〉B and | ψ 〉A of Bob and Alice, respectively.