We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol.
We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol.
We analyze the unidimensional (UD) continuous-variable quantum key distribution protocol in a finite size scenario under realistic conditions. The dependence of the secret key rate on realistic parameters is analyzed numerically. A method of calculating the optimal ratio to divide the data samples in order to achieve the largest secret key rate is proposed. When the data samples are large, the superiority of the UD protocol in data processing becomes apparent. It is expected that the features and methods presented in this paper will aid in the exploration of the latent capacity of the UD protocol as well as the development of further applications.
A unidimensional continuous-variable quantum key distribution protocol with untrusted detection is proposed, where the two legitimate partners send unidimensional modulated or Gaussian-modulated coherent states to an untrusted third party, i.e., Charlie, to realize the measurement. Compared with the Gaussian-modulated coherent-state protocols, the unidimensional modulated protocols take the advantage of easy modulation, low cost, and only a small number of random numbers required. Security analysis shows that the proposed protocol cannot just defend all detectors side channels, but also achieve great performance under certain conditions. Specifically, three cases are discussed in detail, including using unidimensional modulated coherent states in Alice’s side, in Bob’s side, and in both sides under realistic conditions, respectively. Under the three conditions, we derive the expressions of the secret key rate and give the optimal gain parameters. It is found that the optimal performance of the protocol is achieved by using unidimensional modulated coherent states in both Alice’s and Bob’s side. The resulting protocol shows the potential for long-distance secure communication using the unidimensional quantum key distribution protocol with simple modulation method and untrusted detection under realistic conditions.
Abstract Unidimensional continuous variable quantum key distribution (UD-CVQKD) applies Gaussian modulation on one single quadrature of the coherent state. However, in practical experimentations, the finite resolution of modulator driving voltages will result in Gaussian modulation discretization. To investigate its impact on the security of UD-CVQKD, the discretization of amplitude modulation is modeled and analyzed, with the secret key rate formulated against entangling cloner attack. Simulation results demonstrate that despite the performance degradation, UD-CVQKD protocol with discretized amplitude modulation may relax the restriction on correlation parameters to extend the secure region under certain parameters, which can be beneficial to the practicability of UD-CVQKD.
Security of a continuous-variable quantum key distribution protocol based on noisy coherent states and channel is analysed. Assuming that the noise of coherent states is induced by Fred, a neutral party relative to others, we prove that the prepare-and-measurement scheme (P&M) and entanglement-based scheme (E-B) are equivalent. Then, we show that this protocol is secure against Gaussian collective attacks even if the channel is lossy and noisy, and, further, a lower bound to the secure key rate is derived.
We propose a unidimensional two-way continuous-variable quantum key distribution protocol with coherent states, where the sender modulates a single quadrature of the coherent states rather than both quadratures to simplify the structure of a two-way system. Security analysis is performed with a general attack strategy, known as two-mode attack, which helps to reduce limitations in the analysis. The performance of the protocol under all accessible two-mode attacks at fixed distance is illustrated. Further, two typical two-mode attack strategies are obtained from it, which are one-mode attack strategy and optimal two-mode attack strategy. Between them, the one-mode attack is the simplest form of the two-mode attack, while the optimal two-mode attack is the most complicated one. Simulations show that though the system is simplified, the performance of the two-way protocol with unidimensional modulation is still comparable to that of the counterpart with Gaussian modulation even against the optimal two-mode attack when Eve's ability is maximized. Thus, the proposed protocol simplifies the two-way system while guaranteeing its performance to a certain extent. Especially in a practical system with short transmission distance and high excess noise, the protocol has a good application prospect.
We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.