Quantum Inf Process (2017) 16:130
Quantum key agreement protocols with single photon in
both polarization and spatial-mode degrees of freedom
· Wenping Ma
Received: 26 January 2016 / Accepted: 21 March 2017 / Published online: 4 April 2017
© Springer Science+Business Media New York 2017
Abstract In this paper, we propose a three-party and a multi-party quantum key
agreement protocols with single photons in both polarization and spatial-mode degrees
of freedom. Based on the deﬁned collective unitary operations, the participants can
agree on a secure shared key through encoding their sub-secret keys on the particles.
Moreover, the security of our protocols is discussed comprehensively. It is showed that
the presented protocols can defend both the outside attacks and participant attacks. The
efﬁciency analysis also shows that our two protocols can achieve high qubit efﬁciency.
Besides, our protocols are feasible since the preparation and the measurement of single-
photon state in both polarization and spatial-mode degrees of freedom are available
with current quantum techniques.
Keywords Quantum cryptography · Quantum key agreement · Multi-party ·
Single photon · Two degrees of freedom
To achieve secure end-to-end communications in a distributed network, a shared key
between participants is required to support basic secure primitives, such as encryption
and authentication. In classical setting, there are two main methods to obtain a shared
key: the key distribution and the key agreement. In a key distribution protocol, all
Faculty of Software, Fujian Normal University, Fuzhou 350108, China
State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China