Continuous-variable quantum key distribution (CV-QKD) provides an effective way to obtain the high secret key rate, but is limited by practical techniques. To overcome this limitation, we investigate the performance of CV-QKD protocols when non-Gaussian operations are applied to both sides of the channels, including photon subtraction and addition, and photon catalysis. A comparison is also made between Gaussian modulation and non-Gaussian modulation. We show that the optimal transmission distance cannot be improved by non-Gaussian modulation at the sender's side, but it can be improved by single-photon catalysis at the receiver's side. For a given modulation variance that exceeds a certain threshold, the performance of the zero-photon catalysis at the sender's side is the best when compared with other non-Gaussian modulations (except single-photon catalysis at the receiver's side), and it can always reach the optimal distance. Our paper will provide a useful insight for the use of non-Gaussian modulation to other CV-QKD protocols.
Continuous-variable quantum key distribution (CV-QKD) provides an effective way to obtain the high secret key rate, but is limited by practical techniques. To overcome this limitation, we investigate the performance of CV-QKD protocols when non-Gaussian operations are applied to both sides of the channels, including photon subtraction and addition, and photon catalysis. A comparison is also made between Gaussian modulation and non-Gaussian modulation. We show that the optimal transmission distance cannot be improved by non-Gaussian modulation at the sender's side, but it can be improved by single-photon catalysis at the receiver's side. For a given modulation variance that exceeds a certain threshold, the performance of the zero-photon catalysis at the sender's side is the best when compared with other non-Gaussian modulations (except single-photon catalysis at the receiver's side), and it can always reach the optimal distance. Our paper will provide a useful insight for the use of non-Gaussian modulation to other CV-QKD protocols.
The non-Gaussian operation can be used not only to enhance and distill the entanglement between Gaussian entangled states, but also to improve the performance of quantum communications. In this paper, we propose a non-Gaussian continuous-variable quantum key distribution (CVQKD) by using quantum catalysis (QC), which is an intriguing non-Gaussian operation in essence that can be implemented with current technologies. We perform quantum catalysis on both ends of the Einstein-Podolsky-Rosen pair prepared by a sender, Alice, and find that for the single-photon QC-CVQKD, the bilateral symmetrical quantum catalysis performs better than the single-side quantum catalysis. Attributing to characteristics of an integral within an ordered product of operators, we find that the quantum-catalysis operation can improve the entanglement property of Gaussian entangled states by enhancing the success probability of non-Gaussian operation, leading to the improvement of the QC-CVQKD system. As a comparison, the QC-CVQKD system involving zero-photon and single-photon quantum catalysis outperforms the previous non-Gaussian CVQKD scheme via photon subtraction in terms of a secret key rate, maximal transmission distance, and tolerable excess noise.
Quantum key distribution (QKD) with continuous variable (CV) is an effective method for achieving the high key rate, but is also limited to a short transmission distance. To overcome this limitation, some solutions have been proposed, including non-Gaussian operations, such as photon addition and photon subtraction using ideal photon source and number-resolving detection. Here we consider the effect of non-Gaussian operation for realistic photon source and ideal on-off photon detection. In the realistic case, it is shown that the performance of CVQKD can not be improved by both photon-subtraction/addition on the right side before the entangled source reaches the channel and photon-subtraction on the left side preceding the entangled source to the sender Alice before performing heterodyne detection, but be enhanced by the photon addition on the left side in a long distance case. These results may provide a useful reference for quantum information with continuous variable.
Photon subtraction can enhance the performance of continuous-variable quantum key distribution (CV QKD). However, the enhancement effect will be reduced by the imperfections of practical devices, especially the limited efficiency of a single-photon detector. In this paper, we propose a non-Gaussian postselection method to emulate the photon substraction used in coherent-state CV QKD protocols. The virtual photon subtraction not only can avoid the complexity and imperfections of a practical photon-subtraction operation, which extends the secure transmission distance as the ideal case does, but also can be adjusted flexibly according to the channel parameters to optimize the performance. Furthermore, our preliminary tests on the information reconciliation suggest that in the low signal-to-noise ratio regime, the performance of reconciliating the postselected non-Gaussian data is better than that of the Gaussian data, which implies the feasibility of implementing this method practically.
Quantum key distribution (QKD) is fundamentally different from most classical key distribution schemes, such as Diffie-Hellman key exchange, in the sense that no computational complexity assumption is required on the power of adversaries to prove its security. QKD relies on basic laws of quantum physics and it is proven that it can enable highly secure data communication. Such achievements, however, are facing technological problems that have to be resolved in order to provide a viable solution to a large group of customers. While there are discrete-variable QKD schemes, which rely on encoding data in discrete degrees of freedom, such as polarization of single photons, in this thesis, we focus on the continuous-variable QKD (CV-QKD) protocols, in which data is encoded on the quadratures of light. Currently, one of the major drawbacks of CV-QKD is its poor performance at long distances. Nevertheless, such a limitation in CV-QKD can be overcome with the assistance of quantum repeaters that rely on entanglement distillation via noiseless linear amplifiers (NLAs). Such systems can, in principle, offer large secret key rates over long distances. In this thesis, we aim to provide a realistic analysis of a CV-QKD protocol running over quantum scissors (QSs) as realistic NLAs. We will report the obstacles that one could face in realizing CV-QKD in such a scenario. A review of CV-QKD and QS-based NLAs will be given, based on which QS-assisted CV-QKD is proposed. We, particularly, focus on the modelling of the QSs' structure and their effect on the secret key rate aiming to find operational regimes where the performance of the QKD scheme is enhanced. This study paves the way for implementing long-distance CV-QKD protocols that rely on QS/NLA devices over CV quantum repeaters. \n \nIn this thesis, we also consider and account for a realistic analysis of a CV-QKD protocol with non-Gaussian modulation, which is assisted by the means of QSs. We will show that, while we have to deal with similar obstacles as in the Gaussian modulation, we can potentially improve performance of the non-Gaussian modulation protocol. \n \nAs an alternative approach to extend the secure distance of CV-QKD protocols, the last part of this thesis is devoted to presenting realistic threat models for satellite QKD, wherein we consider several eavesdropping scenarios by limiting eavesdroppers' access to the trusted ground and/or satellite stations. In such scenarios, the eavesdropper has only limited access to the sender and/or receiver stations. \nFor example, we will explore the case where an eavesdropper can only receive an attenuated version of the transmitted signals. As well, we will focus on the case where Eve's signals would reach the receiver via a lossy channel inaccessible to the eavesdropper. We show that, in the case of both Gaussian and non-Gaussian protocols, this limitation would allow trusted parties to achieve higher key rates than what can be achieved when unrestricted eavesdropping is possible.
Non-Gaussian operations in continuous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis, and subtraction on squeezed coherent states on CV measurement-device-independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we observe that zero photon catalysis on the two-mode squeezed coherent state (TMSC) is an optimal choice for CV MDI QKD, while single photon subtraction is also a good candidate; both of them offer nearly 70 km of transmission distances. We also derive a single generalized covariance matrix for the aforementioned states which will be useful in several other aspects of CV quantum information processing.
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.