Quantum communication can realize secure information transmission based on the fundamental principles of quantum mechanics. Photon is a crucial information carrier in quantum communication. The photonic quantum communication protocols require the transmission of photons or photonic entanglement between communicating parties. However, in this process, photon transmission loss inevitably occurs due to environmental noise. Photon transmission loss significantly reduces the efficiency of quantum communication and even threatens its security, so that it becomes a major obstacle for practical long-distance quantum communication. Quantum noiseless linear amplification (NLA) is a promising method for mitigating photon transmission loss. Through local operations and post-selection, NLA can effectively increase the fidelity of the target state or the average photon number in the output state while perfectly preserving the encoded information of the target state. As a result, employing NLA technology can effectively overcome photon transmission loss and extend the secure communication distance.

In this paper, the existing NLA protocols are categorized into two types, i.e. the NLA protocols in DV quantum systems and CV quantum systems. A detailed introduction is given to the quantum scissor (QS)-based NLA protocols for single photons, single-photon polarization qubits, and single-photon spatial entanglement in the DV quantum systems. The QS-based NLA can effectively increase the fidelity of the target states while perfectly preserving its encodings. In recent years, researchers have made efforts to study various improvements to the QS-based NLA protocols. In the CV quantum systems, researchers have adopted parallel multiple QS structure and generalized QS to increase the average photon numbers of the Fock states, coherent states and two-mode squeezed vacuum states. In addition to theoretical advancements, significant progress has also been made in the experimental implementations of NLA. The representative experimental demonstrations of QS-based NLA protocols are summarized.

Finally, the future development directions for NLA to facilitate its practical applications are presented. This review can provide theoretical support for practically developing NLA in the future.