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Discrete-modulation measurement-device-independent continuous-variable quantum key distribution with a quantum scissor: exact non-Gaussian calculation

Khatereh Jafari, Mojtaba Golshani, Alireza Bahrampour

Published Mar 4, 2022• 12 citations
Publisher

Abstract

In this paper, we study non-Gaussian discrete-modulated measurement-device-independent continuous-variable quantum key distribution protocol equipped with a proposed quantum scissor at the receiver side. Our suggested scissor truncates all multiphoton number states with four or more photons and amplifies remaining photon number states in a probabilistic way. Using exact non-Gaussian calculation, we find that quantum scissor meliorates the fidelity and entanglement between two legitimate parties Alice and Bob, at long distances. Therefore, quantum scissor enhances the continuous-variable quantum key distribution protocol range. Examination of the system for different values of the excess noise reveals that this improvement disappears at high noisy channels.

DOI
10.1364/oe.452654

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In this paper, we study non-Gaussian discrete-modulated measurement-device-independent continuous-variable quantum key distribution protocol equipped with a proposed quantum scissor at the receiver side. Our suggested scissor truncates all multiphoton number states with four or more photons and amplifies remaining photon number states in a probabilistic way. Using exact non-Gaussian calculation, we find that quantum scissor meliorates the fidelity and entanglement between two legitimate parties Alice and Bob, at long distances. Therefore, quantum scissor enhances the continuous-variable quantum key distribution protocol range. Examination of the system for different values of the excess noise reveals that this improvement disappears at high noisy channels.
It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive.
It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive.
This study presents a closed-form expression that characterizes the output state of a continuous variable quantum key distribution protocol in the presence of both ideal and realistic two photon quantum scissor. Using non-Gaussian computations, we discovered that the ideal quantum scissor improves entanglement between Alice and Bob, even when they are separated by large distances. As a result, the addition of quantum scissors broadens the range of continuous variable quantum key distribution protocols. Additionally, non-ideal quantum scissors' efficiency becomes more significant as the modulation variance of the input state increases. Finally, keep in mind that the benefits of these changes tend to reduce in noisy channels, when the system is inspected under varied amounts of excess noise.
The method of improving the performance of continuous-variable quantum key distribution protocols by postselection has been recently proposed and verified. In continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocols, the measurement results are obtained from untrusted third party Charlie. There is still not an effective method of improving CV-MDI QKD by the postselection with untrusted measurement. We propose a method to improve the performance of coherent-state CV-MDI QKD protocol by virtual photon subtraction via non-Gaussian postselection. The non-Gaussian postselection of transmitted data is equivalent to an ideal photon subtraction on the two-mode squeezed vacuum state, which is favorable to enhance the performance of CV-MDI QKD. In CV-MDI QKD protocol with non-Gaussian postselection, two users select their own data independently. We demonstrate that the optimal performance of the renovated CV-MDI QKD protocol is obtained with the transmitted data only selected by Alice. By setting appropriate parameters of the virtual photon subtraction, the secret key rate and tolerable excess noise are both improved at long transmission distance. The method provides an effective optimization scheme for the application of CV-MDI QKD protocols.
Security of continuous-variable quantum key distribution with four-state protocol based on discrete modulation of noisy coherent states is analyzed. Combing discrete modulation and reverse reconciliation, this protocol can be used for long distance cryptography. There is a small difference between the state Alice sends in the discrete modulation protocol and the Gaussian modulation protocol, and it can be treated as excess noise and loss in the channel. As Alice cannot do a precise modulation, she will induce noise to the coherent state. We look this noise as the source noise and derive a lower bound to the secure key rate assuming the eavesdropper cannot benefit from the noise in the source. For avoiding the fast and random phase locking between the signal and local oscillator in experiment, we also analyze the security of four-state protocol using no-switching scheme.
We propose a new scheme to enhance the performance of the Gussian-modulated coherent-state continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) system via quantum scissors (QS) operation at Bob’s side. As an non-deterministic amplifying setup, we firstly introduce the QS-enhanced CV-MDI-QKD protocol and then investigate the success probability of the QS operation in accordance with the equivalent one-way scheme. Afterwards, we investigate the effect of the QS operation on the proposed scheme and analyze the performance of the QS-enhanced CV-MDI-QKD system under the extreme asymmetric circumstance. Simulation results show that the QS operation can indeed improve the performance of the CV-MDI-QKD system considerably. QS-enhanced CV-MDI-QKD protocol outperforms the original CV-MDI-QKD protocol in both the maximum transmission distance and the secret key rate. Moreover, the better the performance of QS operation, the more significant the improvement of performance of the system.