Tight finite-key analysis for quantum key distribution without monitoring signal disturbance

Unlike traditional communication, quantum key distribution (QKD) can reach unconditional security and thus attracts intensive studies. Among all existing QKD protocols, round-robin-differential-phase-shift (RRDPS) protocol can be running without monitoring signal disturbance, which significantly simplifies its flow and improves its tolerance of error rate. Although several security proofs of RRDPS have been given, a tight finite-key analysis with a practical phase-randomized source is still missing. In this paper, we propose an improved security proof of RRDPS against the most general coherent attack based on the entropic uncertainty relation. What’s more, with the help of Azuma’s inequality, our proof can tackle finite-key effects primely. The proposed finite-key analysis keeps the advantages of phase randomization source and indicates experimentally acceptable numbers of pulses are sufficient to approach the asymptotical bound closely. The results shed light on practical QKD without monitoring signal disturbance.

Lévy Processes and Benfordʼs Law

This chapter examines Lévy processes (LPs). These processes can be thought of as random walks in continuous time, having independent and stationary increments, with the assumption that the characteristic function of the state of an LP at time 1 satisfies a certain “Standard Condition” (SC). Exponential Lévy processes (ELPs) in particular are quite attractive for modeling many phenomena. The chapter begins by explaining LPs in more detail, introducing the basic notions as well as providing examples of Lévy processes. It then uses a certain variant of the Poisson Summation Formula to arrive at convergence results for the expectations of certain normalized functionals of the significand of an ELP and obtain, using Azuma's inequality for martingales, large deviation results for these functionals. From here, the chapter calculates the a.s. (almost surely) convergence of normalized functionals and discusses further related conditions and theorems.

The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

Extending Blackwell's Strengthening of Azuma's Martingale Inequality

We extend a recent strengthening of Azuma's inequality to allow for a non symmetric bound on the martingale differences.