A Measurement Device Independent Quantum Key Distribution protocol in the service of three users

Abstract

Quantum Key Distribution (QKD) is the only theoretically proven method for secure key distribution between two users. In this work, we propose and analyze a Measurement Device Independent (MDI) protocol designed to distribute keys among three users in a pairwise manner. Each user randomly selects a basis, encodes bit values in the phase of coherent states, and sends the resulting pulses to a central measurement unit (MU) composed of three beam splitters and three photon detectors. When the three pulses arrive simultaneously at the MU and under the condition of successful detection of photons, a key bit is distributed to at least one pair of users. This protocol extends the foundational phase-encoding MDI protocol introduced by [K. Tamaki, et al., Phys. Rev. A 85, 042307 (2012)] to three users, but this comes at the cost of introducing a systematic error in the implementation of the honest protocol.