Bidirectional transfer of quantum information for unknown photons via cross-Kerr nonlinearity and photon-number-resolving measurement

We propose an arbitrary controlled-unitary (CU) gate and a bidirectional transfer scheme of quantum information (BTQI) for unknown photons. The proposed CU gate utilizes quantum non-demolition photon-number-resolving measurement based on the weak cross-Kerr nonlinearities (XKNLs) and two quantum bus beams; the proposed CU gate consists of consecutive operations of a controlled-path gate and a gathering-path gate. It is almost deterministic and is feasible with current technology when a strong amplitude of the coherent state and weak XKNLs are employed. Compared with the existing optical multi-qubit or controlled gates, which utilize XKNLs and homodyne detectors, the proposed CU gate can increase experimental realization feasibility and enhance robustness against decoherence. According to the CU gate, we present a BTQI scheme in which the two unknown states of photons between two parties (Alice and Bob) are mutually swapped by transferring only a single photon. Consequently, by using the proposed CU gate, it is possible to experimentally implement the BTQI scheme with a certain probability of success.