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Frontiers in Optics

Mutually unbiased bases for time-bin qudits

Joseph M. Lukens, Nurul T. Islam, Charles Ci Wen Lim, Daniel J. Gauthier

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We introduce a method for generation and detection of mutually unbiased bases for time-bin qudits employing electro-optic phase modulator – coded fiber Bragg grating pairs. Our approach uses one spatial mode and can switch rapidly between bases.
DOI
10.1364/fio.2018.jw3a.66

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We propose a method for implementing mutually unbiased generation and measurement of time-bin qudits using a cascade of electro-optic phase modulator–coded fiber Bragg grating pairs. Our approach requires only a single spatial mode and can switch rapidly between basis choices. We obtain explicit solutions for dimensions d = 2, 3, and 4 that realize all d + 1 possible mutually unbiased bases and analyze the performance of our approach in quantum key distribution. Given its practicality and compatibility with current technology, our approach provides a promising springboard for scalable processing of high-dimensional time-bin states.
In this paper, we propose several fiber Bragg gratings (FBGs) based on both weak coherent state (WCS) and entanglement-assisted (EA) multidimensional QKD (MQKD) protocols with mutually unbiased bases (MUBs) derived from the complex Hadamard matrices. We also propose how to implement them by using FBGs with orthogonal impulse responses, derived from Slepian sequences. The proposed FBG-based protocols are capable of simultaneously achieving unprecedented spectral efficiency and secret-key rates in long-distance quantum communication. Regarding the WCS protocols, random base selection and FGB-MUB-based protocols are introduced. Regarding EA protocols, we introduce a generic class of FBG-based N-dimensional protocols and describe the corresponding FBG-based encoders and decoders. The security analysis of the proposed MQKD protocols is further performed by taking into account FBG fabrication imperfections, modeled by the L-neighbor model. It has been shown that the proposed MQKD protocols significantly outperform the conventional two-dimensional QKD protocols, and impose less stringent bandwidth requirements compared to multidimensional time-frequency and time-bin protocols.