Security of a new two-way continuous-variable quantum key distribution protocol

The original two-way continuous-variable quantum-key-distribution (CV QKD) protocols [S. Pirandola, S. Mancini, S. Lloyd, and S. L. Braunstein, Nature Physics 4, 726 (2008)] give the security against the collective attack on the condition of the tomography of the quantum channels. We propose a family of new two-way CV QKD protocols and prove their security against collective entangling cloner attacks without the tomography of the quantum channels. The simulation result indicates that the new protocols maintain the same advantage as the original two-way protocols whose tolerable excess noise surpasses that of the one-way CV-QKD protocol. We also show that all sub-protocols within the family have higher secret key rate and much longer transmission distance than the one-way CV-QKD protocol for the noisy channel.Comment: 19 pages, 4 figures, accepted for publication in International Journal of Quantum Informatio

Improvement of two-way continuous-variable quantum key distribution using optical amplifiers

The imperfections of a receiver's detector affect the performance of two-way continuous-variable quantum key distribution protocols and are difficult to adjust in practical situations. We propose a method to improve the performance of two-way continuous-variable quantum key distribution by adding a parameter-adjustable optical amplifier at the receiver. A security analysis is derived against a two-mode collective entangling cloner attack. Our simulations show that the proposed method can improve the performance of protocols as long as the inherent noise of the amplifier is lower than a critical value, defined as the tolerable amplifier noise. Furthermore, the optimal performance can approach the scenario where a perfect detector is used.Comment: 14 pages, 7 figure

Characterization of domains of self-adjoint ordinary differential operators of any order, even or odd

We characterize the domains of very general ordinary differential operators of any order, even or odd, with complex coefficients and arbitrary deficiency index

An improved two-way continuous-variable quantum key distribution protocol with added noise in homodyne detection

We propose an improved two-way continuous-variable quantum key distribution (CV QKD) protocol by adding proper random noise on the receiver's homodyne detection, the security of which is analysed against general collective attacks. The simulation result under the collective entangling cloner attack indicates that despite the correlation between two-way channels decreasing the secret key rate relative to the uncorrelated channels slightly, the performance of the two-way protocol is still far beyond that of the one-way protocols. Importantly, the added noise in detection is beneficial for the secret key rate and the tolerable excess noise of this two-way protocol. With the reasonable reconciliation efficiency of 90%, the two-way CV QKD with added noise allows the distribution of secret keys over 60 km fibre distance.Comment: 12 pages, 6 figure

The discreteness of spectrum for higher-order differential operators in the weighted function spaces

In this paper we consider the discreteness of spectrum for higher-order differential operators in the weighted function spaces. Using the method of the embedding theorems of weighted Sobolev spaces $H_p^n$ in weighted spaces $L_{s,r}$, we obtain a new sufficient and necessary condition to ensure that the spectrum is discrete, which can be easily used to judge the discreteness of some differential operators. 10.1017/S000497271200068