Investigation on entanglement robustness of continuous variable EPR entangled state distributed over optical fiber channel

Einstein-Podolsky-Rosen (EPR) entangled state light field at the telecommunication wavelength of 1.5 μm is an important quantum source for the realization of continuous variable quantum information processing and some quantum protocols over optical fiber channel. When the EPR entangled state light field is distributed over the optical fiber channel, the disentanglement is always occured because the the EPR entangled state interacts with the fiber channel. It affects the performance of quantum information processing. In this paper, we theoretically calculated the positive partial transposition (PPT) of the entangled state distributed over the optical fiber channel in the single-channel and dual-channel distribution scheme, respectively. Three types of initial entangled light field was considered and analyzed, including an initial EPR entangled state, an EPR entangled state with asymmetric quadratures and an EPR entangled state with asymmetric modes. Furthermore, the influence of the extra noise in the optical fiber on the transmission distance of EPR entangled state over the optical fiber channel was investigated. In the single-channel scheme or dual-channel scheme, the extra noise in the optical fiber channel leads to disentanglement of the entangled state light field, and the transmission distance of EPR entangled state over the optical fiber channel decreases rapidly with the increase of the extra noise. For the sake of maintain the robustness of EPR entangled states in lossy optical fiber channels, the dual-channel scheme has more stringent requirements on the correlation quadrature symmetry and purity of the initial entangled state than the single-channel scheme. In the single fiber noise channel scheme, the maximum transmission distance and the robustness of the EPR entangled states with asymmetric modes is not sensitive to the asymmetry between modes. The change of asymmetry between modes does not lead to disentangle. The maximum transmission distance does also not change. However, the decrease of asymmetry between modes leads to disentangle in the double fiber noise channels scheme scheme. The maximum transmission distance is reduced and entanglement sudden death occurs. The results will lay a foundation for continuous variables quantum information processing based on optical fiber, such as realizing continuous variables quantum communication over optical fiber and constructing metropolitan quantum network over optical fiber.