In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are improved.

Spatial mode-division multiplexing is emerging as a potential solution to further increasing optical fiber capacity and spectral efficiency. We report a dual-mode, dual-polarization transmission method based on mode-selective excitation and detection over a two-mode fiber. In particular, we present 107 Gbit/s coherent optical OFDM (CO-OFDM) transmission over a 4.5 km two-mode fiber using LP01 and LP11 modes in which mode separation is performed optically.