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Enhancing the Secure Key Rate in a Quantum Scissors-Based Continuous Variable Quantum Key Distribution Protocol

Jafari, Khatereh | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57023 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Bahrampour, Alireza
  7. Abstract:
  8. Continuous-variable quantum key distribution (CV-QKD) protocols, that share an unconditionally secure key between at least two legitimate parties, are based on the modulation of information on the continuous characteristics of light. CV-QKD is low-cost, has a high rate, and is compatible with conventional technology. However, one of the major drawbacks of CV-QKD is its poor performance at long distances. Such a limitation can be overcome with the assistance of noiseless linear amplifiers (NLAs). In this thesis, we aim to use Quantum scissor (QS), as a realistic NLA, to overcome this limitation. To this end, we suggested a three-photon QS that truncates all multiphoton number states with four or more photons and amplifies remaining photon number states in a probabilistic way. This setup works ideally for superpositions of up to three photons, but, if it is used on coherent states it will not amplify perfectly. The fidelity of the amplification obtained by this suggested QS is as good as that obtainable with a network of six one-photon, or a network of two two-photon amplifiers. Moreover, the probability that this generalized QS works is of the same order of magnitude as that for four one-photon, or two two-photon amplifiers. Next, we investigate non-Gaussian discrete-modulated measurement-device-independent CV-QKD protocol equipped with a suggested three-photon QS. Given that the QS is a non-Gaussian operation, using exact calculation, we find that this QS meliorates the fidelity and entanglement between two legitimate parties Alice and Bob, at long distances. Accordingly, QS enhances the CV-QKD protocol range. Investigation of the system for different values of the excess noise reveals that this improvement disappears when we deal with a high noisy channel. In the following, we peruse how the combination of a QS and zero-photon catalysis (ZPC) intensifies the range and the fidelity of a CV-QKD protocol. Our results reveal that QS, by noiseless amplification of the final state, significantly boosts both the secure key rate and the fidelity of teleportation at long distances. At negligible values of excess noise, there is an optimal strength of the ZPC operation, that maximizes the secure distance of the protocol. Moreover, our investigation of the proposed protocol with a nonzero value of excess noise and for limited values of modulation strength, reveals that the fidelity generally increases with ZPC, as opposed to the range, which decreases with this Gaussian operation. Finally, in order to find the optimal parameters, by using Gaussian modulation instead of discrete modulation, and replacing the three-photon QS with one-photon QS in the previous protocol, we derived a closed-form expression for the output state of a CV-QKD protocol in the presence of ZPC and QS. Then, we used a direct search algorithm to find the appropriate values of input state and QS parameters, which considerably enhance the range and the fidelity of a CV-QKD protocol. In the case of a pure loss channel, the largest range of the protocol is only 6.5% less than the fundamental limit of repeaterless quantum communication. In addition, we find that there is a trade-off between range and fidelity, and much higher fidelity can be obtained if someone ignores a smaller amount of the protocol range
  9. Keywords:
  10. Continuous Variable Quantum Key Distribution (CV-QKD) ; Noise Less Amplification ; Discrete Multi-Tone (DMT)Modulation ; High Fidelity ; Noiseless Linear Amplifier ; Zero-Photon Catalysis ; Quantum Scissors

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