High-efficient noiseless linear amplification of the single-photon spatial W state

Single photon spatial-mode entanglement is an important resource in quantum communication, which is widely used in quantum teleportation, quantum secure direct communication, quantum repeater, quantum key distribution and so on. The single-photon spatial-mode W state is an important single-photon multi-mode entanglement. However, when distributing the single-photon spatial-mode W state in practical imperfect quantum channels, the transmission loss caused by the channel noise will cause the photon to decay exponentially with the growth of channel length. Based on quantum non-cloning theorem, we cannot accurately copy the quantum state. The photon transmission loss will largely reduce quantum communication's efficiency, and even threaten its security. As a result, the photon transmission loss is a big obstacle for the practical development of long-distance quantum communication. Noiseless linear amplification (NLA) is a promising method to solve the photon transmission loss problem, which can herald the existence of the target photon without destroying it. In order to protect the single-photon spatial-mode W state from photon transmission loss, we propose an NLA protocol scheme for the single-photon spatial-mode W state based on the high-efficient quantum scissor (QS) with local squeezing operation. In this protocol, each remote communication party needs to operate a high-efficient QS with local squeezing operation simultaneously. Only when all the quantum scissors are successfully operated, the NLA protocol for the single-photon spatial-mode W state will be successful. By adjusting the transmittance of the variable beam splitter (VBS) in each QS, one can increase the fidelity of the target single-photon spatial-mode W state. The total success probability and amplification factor of our NLA protocol depend on the transmittance of VBS, the photon transmission efficiency, and the squeezing parameter. Comparing with the NLA protocol with conventional QSs without the local squeezing operation, our NLA protocol can obtain the higher amplification factor by introducing the local squeezing operation in each QS, and thus obtains the higher amplification efficiency. Our NLA protocol requires the linear optical elements, such as the BS, PBS, and VBS. Meanwhile, it requires the local squeezing operation, which is the key technology of our NLA protocol. The local squeezing operation is an important technology in continuous-variable quantum information processing. During the past few years, some attractive progress on the local squeezing operation has been reported. For example, in 2006, Suzuki et al. observed -7.2 +/- 0.2 dB quadrature squeezing at 860nm by using a subthreshold continuous-wave pumped optical parametric oscillator with a periodically poled KTiOPO4 crystal as a nonlinear optical medium. In 2007, a squeezing level of -9.01 +/- 0.14 dB and an antisqueezing level of +15.12 +/- 0.14 dB were achieved using a local oscillator phase locked in a homodyne measurement. Recently, the efficient generation of quadrature squeezing from biexcitonic parametric gain in atomically thin semiconductors has been theoretically demonstrated. Based on the attractive progress, our NLA protocol with the local squeezing technology may be realized in the near future.