Research On Heralded Amplification Of The Quantum State Encoding In Multi-degrees Of Freedom

Quantum informatics is an interdisciplinary fusion of quantum mechanics and informatics.Quantum mechanics is a science describing the laws of the movement of microscopic particles.Many physical phenomena that cannot be explained by classical mechanics can be well explained by quantum mechanics.Nowadays,a large number of experiments have proved the correctness of quantum mechanics theory,and more and more scientists around the world have become interested in the research of quantum mechanics.Entanglement is one of the most abstract concepts in quantum physics.It is the main resource of quantum communication,such as quantum teleportation,quantum secure direct communication,quantum repeater,quantum key distribution and so on.However,when transmitting photons or distributing entanglement in a quantum channel that is actually imperfect,the transmission loss caused by environmental noise will cause the propagation of photons in the fiber to exhibit exponential attenuation with the increase of the channel length.Due to the existence of quantum non-cloning theorem,we cannot accurately copy quantum states,which makes the transmission of photons have a limit distance.In addition,even within the limit distance,the photon has a certain probability of loss,which will make the single photon state into a mixed state of single photon and empty state with a certain probability.Quantum heralded amplification,also known as noiseless linear amplification(NLA),is an effective method to solve the problem of photon transmission loss.Multi-degree-of-freedom coding refers to the simultaneous coding of multiple degrees of freedom of photons.Because multi-degree-of-freedom coded photons(qudit)can effectively expand the channel capacity,they have received extensive attention from researchers in recent years.However,qudit also inevitably suffers from transmission loss during the distribution of the actual noise quantum channel.The previous NLA protocols are aimed at the situation where the photon has encoded information in only one degree of freedom.The first work in this paper uses the assistance of polarized single photon to propose a NLA scheme for the spatial entangled state of qudit coded in two degrees of freedom,polarization and time.Our NLA scheme can also be applied to resist both complete and partial loss of photons.Executing the NLA protocol can not only increase the fidelity of the qudit's single-photon space entangled state,but also solve its decoherence problem in space degrees of freedom.Another work in this paper is to design a recyclable amplification scheme that can resist single photon entangled states that are completely lost and partially lost at the same time.The protocol mainly relies on quantum nondemolition detection gates constructed with the help of cross-Kerr nonlinearity to achieve nondemolition measurement of photons.If the scheme fails,the extracted single photon entangled state can be reused.By running the NLA scheme again,we can still extract high-fidelity single-photon entangled states.After the scheme is successful,we can continue to run the scheme to further improve the fidelity of the single-photon entangled state.This scheme can effectively increase the success probability and amplification factor of amplification.The two NLA schemes in this paper have important application prospects in future quantum information applications.