We present two deterministic quantum entanglement distribution protocols for a four-photon Dicke polarization entangled state resorting to the frequency and spatial degrees of freedom, which are immune to an arbitrary collective-noise channel. Both of the protocols adopt the X homodyne measurement based on the cross-Kerr nonlinearity to complete the task of the single-photon detection with nearly unit probability in principle. After the four receivers share the photons, they add some local unitary operations to obtain a standard four-photon Dicke polarization entangled state.
We present an efficient quantum entanglement distribution over an arbitrary collective-noise channel. The basic idea in the present scheme is that two parties in quantum communication first transmit the entangled states in the frequency degree of freedom which suffers little from the noise in an optical fiber. After the two parties share the photon pairs, they add some operations and equipments to transfer the frequency entanglement of pairs into the polarization entanglement with the success probability of
100. Finally, they can get maximally entangled polarization states with polarization independent wavelength division multiplexers and quantum frequency up-conversion which can erase distinguishability for frequency. Compared with conventional entanglement purification protocols, the present scheme works in a deterministic way in principle. Surprisingly, the collective noise leads to an additional advantage.
The encoding in multiple degrees of freedom can effectively improve the performance of current quantum key distribution, but the collective channel noise reduces the security of these proposals. In this article, we propose a high capacity quantum key distribution with single-photon in polarization and spatial-mode degrees of freedom, and protect the quantum states against the general collective noise by error-rejection in two degrees of freedom and quantum channel multiplexing. The states transmission and measurements in the presented quantum key distribution can be realized deterministically. The security analysis under the intercept-measure-resend eavesdropping and controlled-NOT operation eavesdropping attacks is conducted to verify the security, and the secure key rate analysis proves the efficiency of our proposal. These advantages make our proposal useful in practical quantum communication under current experimental conditions.