Remote Implementation of Particular Subsets of Operations in two Degrees of Freedom

Hyperentanglement of photon systems is a fascinating resource in long-distance quantum information processing and communication for its improvement to the channel capacity. Remote implementation of quantum operation (RIO) using a hyperentangled state has attracted much attention for its critical role in many quantum applications. In this study, a protocol for the remote implementation of particular subsets of operations exploiting a pair of photons hyperentangled in their polarization and time-bin degrees of freedom (DOFs) is presented. The core of this scheme is to construct polarization and time-bin parity-check quantum nondemolition detectors (QNDs), which mainly rely on the effective cross-Kerr nonlinear interaction and X homodyne measurements. The efficiency of the scheme is calculated in terms of bits of transmission and consumption. Compared with the RIO using the polarization-spatial-mode hyperentangled state, the present scheme saves resources since there is no requirement for two paths for each photon. Further, given some applicable experimental parameters, the fidelity due to the effect of decoherence in the circuits is analyzed, and the result demonstrates a high fidelity in the presence of photon dissipation. Since the time-bin DOF is more robust over a channel, especially from space to earth, this RIO protocol presents a promising approach for building a global quantum-communication network.