Indistinguishable encoding for bidirectional quantum key distribution: Theory to experiment

¹ Department of Physics, International Islamic University Malaysia (IIUM), Jalan Sultan Ahmad Shah, Bandar Indera Mahkota - 25200 Kuantan, Pahang, Malaysia
² Institute of Mathematical Research (INSPEM), University Putra Malaysia - 43400 UPM Serdang, Selangor, Malaysia

Received: 10 June 2017
Accepted: 3 February 2018

Abstract

We present a bidirectional quantum key distribution protocol with minimal encoding operations derived from the use of only two “nonorthogonal” unitary transformations selected from two mutually unbiased unitary bases. Differently from many bidirectional protocols, these transformations are indistinguishable in principle for a single use. Along with its decoding procedure, it is unique compared to its “orthogonal encoding” predecessors. Given the nature of such protocols where key rates are usually dependent on two different types of error rates, we define a more relevant notion of security threshold for such protocols to allow for proper comparisons to be made. The current protocol outperforms its predecessor in terms of security as the amount of information an eavesdropper can glean is limited by the indistinguishability of the transformations. We further propose adaptations for a practical scenario and report on a proof of concept experimental scheme based on polarised photons from an attenuated pulsed laser for qubits, demonstrating the feasibility of such a protocol.