Abstract A single-photon qudit encoded in more than one degree of freedom (DOF) can effectively enlarge a single photon’s capacity and has great potential for applications in future high-capacity quantum communication fields. During the photon transmission in practical noisy channels, photon qudits may suffer from photon transmission loss, which largely limits their application. In this paper, we propose a practical noiseless linear amplification (NLA) protocol for protecting the single-photon qudit encoded in polarization and double-longitudinal momentum DOFs. This NLA adopts the imperfect entangled state generated from a practical spontaneous parametric down-conversion (SPDC) source as the auxiliary state and can be realized under current experimental conditions. After performing the NLA protocol, the fidelity of the target single-photon qudit can be increased and the encoded information in all DOFs can be well preserved. We show the adoption of the imperfect entangled state generated from SPDC source is superior to that of the imperfect single-photon state from a practical heralded single-photon source. Our NLA protocol has application potential in current and future quantum communications.
Abstract A single-photon qudit encoded in more than one degree of freedom (DOF) can effectively enlarge a single photon’s capacity and has great potential for applications in future high-capacity quantum communication fields. During the photon transmission in practical noisy channels, photon qudits may suffer from photon transmission loss, which largely limits their application. In this paper, we propose a practical noiseless linear amplification (NLA) protocol for protecting the single-photon qudit encoded in polarization and double-longitudinal momentum DOFs. This NLA adopts the imperfect entangled state generated from a practical spontaneous parametric down-conversion (SPDC) source as the auxiliary state and can be realized under current experimental conditions. After performing the NLA protocol, the fidelity of the target single-photon qudit can be increased and the encoded information in all DOFs can be well preserved. We show the adoption of the imperfect entangled state generated from SPDC source is superior to that of the imperfect single-photon state from a practical heralded single-photon source. Our NLA protocol has application potential in current and future quantum communications.
Single-photon entanglement (SPE) is an important source in quantum communication. In this paper, we put forward a single-photon-assisted noiseless linear amplification protocol to protect the SPE of an arbitrary polarization–time-bin qudit from the photon transmission loss caused by the practical channel noise. After the amplification, the fidelity of the SPE can be effectively increased. Meanwhile, the encoded polarization–time-bin features of the qudit can be well preserved. The protocol can be realized under the current experimental conditions. Moreover, the amplification protocol can be extended to resist complete photon loss and partial photon loss during the photon transmission. After the amplification, we can not only increase the fidelity of the target state, but also solve the decoherence problem simultaneously. Based on the above features, our amplification protocol may be useful in future quantum communication.
Abstract Noiseless linear amplification (NLA) is a crucial method to solve the photon transmission loss problem. However, most NLA protocols require an ideal auxiliary single-photon source, which is unavailable under current experimental condition. Meanwhile, their heralded amplification performance is relatively low. For enhancing the feasibility and amplification performance of the NLA, in this paper, we propose an efficient NLA protocol with a practical imperfect auxiliary single-photon source. We introduce the local-quadrature squeezing operation into the NLA protocol, which can effectively increase its amplification factor. This NLA protocol only uses some common linear-optical elements, the practical imperfect auxiliary single-photon source, and imperfect single-photon detectors, so that it is easy to implement under the existing experimental condition. It may have important applications in the future quantum information processing field.
Quantum communication is based on the basic principles of quantum mechanics such as the Heisenberg uncertainty and the no-cloning theorem. Quantum communication can detect the eavesdropping, so that it has unconditional security in theory. Coherent state is an important continuous-variable resource in the quantum communication field. The hyper-encoded coherent states mean encoding in two or more degrees of freedom (DOFs) of each photon in the coherent state, which can increase the capacity of single photon and has potential applications in future high-capacity quantum communication field. However, during practical applications, the channel noise may cause photon transmission loss, which will largely reduce quantum communication’s efficiency, even threaten its security. As a result, the photon transmission loss largely limits the applications of the hyper-encoded coherent states. The noiseless linear amplification (NLA) is a promising method to solve the photon transmission loss problem. However, no existing NLA schemes can be used for the hyper-encoded coherent states. In the paper, we propose an NLA protocol for arbitrary polarization-time-bin hyper-encoded coherent states assisted by auxiliary single photons. This NLA protocol adopts the quantum scissor (QS) devices in the parallel structure. The protocol first splits the input coherent state into N paths with the help of the first beam splitter array, which makes the coherent state in each path be a weak coherent state. Then, it applies the QS in each path. Only when the QS in each path obtains the successful photon-detector response, the whole NLA protocol will be successful. In this case, the output states in all paths will be finally converged into one output path with the help of the second beam splitter array. By adjusting the transmittance of the variable beam splitters in each QS, the NLA protocol can increase the average photon number of the output coherent state, and thus realize the amplification of the coherent state. Meanwhile, the hyper-encoded features in the polarization and time-bin DOFs can be perfectly preserved. Our NLA protocol only requires the common optical elements, so that it can be realized under current experimental conditions. Then, we analyze the performance of our NLA protocol with practical experimental conditions. First, the NLA protocol requires the photon-number-resolving detectors in theory, which are unavailable under practical experimental conditions. With practical imperfect photon detectors, which cannot distinguish the input photon number and have relatively low detection efficiency, the total success probability of the NLA protocol will decrease. Meanwhile, some unwanted disturb items may be introduced into the output state with a small probability, so that the fidelity of the target coherent state in the output state will decrease. Second, the NLA protocol requires an infinite N in theory. In practical experiments, we can only choose a finite N. In this way, besides the amplification, the NLA protocol will perform the N-photon truncation of the coherent state. With the growth of N, the fidelity of the output state will increase, but the total success probability of this NLA protocol will decrease. In conclusion, our NLA protocol can realize the amplification of the polarization-time-bin hyper-encoded coherent state and preserve the hyper-encoded features of the photons. Meanwhile, it can be realized under current experimental conditions. Our protocol has application potential in the future quantum communication field.
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.
Abstract A single photon is the basic building block in quantum communication. However, it is sensitive to photon loss. In this paper, we discuss a linear-optical amplification protocol for protecting a single photon with a practical spontaneous parametric down-conversion (SPDC) source. Our protocol revealed that in a practical experimental condition, the amplification using entanglement as an auxiliary is more powerful than the amplification using a single photon as an auxiliary, for the vacuum state in the SPDC source does not disturb the amplification and can be eliminated automatically. Moreover, the weak SPDC source will become another advantage to benefit the amplification, as the double-pair emission error can be decreased. Our protocol may be useful in future quantum cryptography, especially in the device-independent quantum key distribution.
Heralded noiseless amplification is beneficial in overcoming transmission photon loss in a noisy quantum channel. We propose a single-photon-assisted heralded noiseless amplification protocol of the single-photon entanglement (SPE), where the single-photon qubit has an arbitrary unknown polarization feature. We focus on both the complete and partial photon loss during the transmission process. After the amplification, the parties can recover the pure less-entangled SPE into a maximally entangled SPE and increase its fidelity. Moreover, the polarization feature of the single-photon qubit will be well preserved and not be leaked. Our protocol can be realized under our current experimental condition. Based on the features above, our protocol may be useful in the quantum secure communication schemes that encode information in the polarization degree of freedom of photons.