Asymptotic Security of Continuous-Variable Quantum Key Distribution with a Discrete Modulation

Shouvik Ghorai,Anthony Leverrier,Eleni Diamanti,Philippe Grangier

doi:10.1103/physrevx.9.021059

Abstract

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.

Highlights

Quantum key distribution (QKD) is the task of establishing a secret key between two distant parties, Alice and Bob, who can access an untrusted quantum channel and an authenticated classical channel [1]
We present a major step towards the full security of CVQKD with a discrete modulation, by introducing a new proof technique that establishes a lower bound valid against arbitrary collective attacks, in the asymptotic limit of infinitely long keys
We give a general technique to derive a lower bound on the secret key rate of CVQKD with a discrete modulation and apply it to the case of the QPSK modulation

Summary

Introduction

Quantum key distribution (QKD) is the task of establishing a secret key between two distant parties, Alice and Bob, who can access an untrusted quantum channel and an authenticated classical channel [1]. The first QKD protocol, BB84, was invented by Bennett and Brassard and requires Aliceptffioffi send qubit states frompffiffi the set fj0i; j1i; jþi 1⁄4 ð1= 2Þðj0i þ j1iÞ; j−i 1⁄4 ð1= 2Þðj0i − j1iÞg through the quantum channel, and Bob to perform a measurement in one of the two bases fj0i; j1ig or fjþi; j−ig. This provides them with some correlated data, which can be distilled into a secret key, provided that the correlations are large enough [2]. In CVQKD protocols, information is encoded on the quadratures of the quantized electromagnetic field: Alice

Objectives

Discussion

Conclusion