Loss-tolerant concatenated Bell-state measurement with encoded coherent-state qubits for long-range quantum communication

Abstract

The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly deterministic nature of the Bell-state measurement (BSM). However, its nonorthogonality incurs difficulties such as the failure of the BSM. One may use a large amplitude (α) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes (|α|⪅2), which simultaneously suppresses both failures and dephasing in the BSM procedure. We numerically show that the CBSM scheme achieves a success probability arbitrarily close to unity for appropriate values of α and sufficiently low photon loss rates (e.g., ⪅5%). Furthermore, we verify that the quantum repeater scheme exploiting the CBSM scheme for quantum error correction enables one to carry out efficient long-range quantum communication over 1000 km. We show that the performance is comparable to those of other up-to-date methods and even exceeds them in some cases. Finally, we present methods to prepare logical qubits under modified parity encoding, and we implement elementary logical operations, which consist of several physical-level ingredients such as generation of superpositions of coherent states (SCSs) and elementary gates under the coherent-state basis. We then estimate the effects of imperfect physical-level elements on the performance of the scheme. Our work demonstrates that the encoded coherent-state qubits in free-propagating fields provide an alternative route to fault-tolerant information processing, especially to long-range quantum communication.