Characterizing Turbulence-Induced Decay of Mutual Unbiasedness of Complementary Bases Relevant to Propagated Photonic Spatial-Mode States

• Published in: IEEE access Vol. 7; pp. 108761 - 108767
• Main Authors: Chen, Chunyi, Yang, Huamin
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Angular momentum; Anisotropic magnetoresistance; Anisotropy; atmospheric turbulence; complementary bases; Correlation; Decay; Indexes; Mutual unbiasedness; Optical distortion; Optical propagation; photonic spatial-mode state; Photonics; Propagation modes; Quantum cryptography; quantum key distribution; Turbulence
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2931554

Mutually complementary bases are crucial to secure quantum key distribution (QKD). By aiming at free-space QKD with use of spatially structured photons, the effect of turbulence on the mutual unbiasedness of two complementary bases relevant to photonic orbital-angular-momentum (OAM) modes is modeled theoretically, with novel insightful expressions and physical explanations yielded. For two complementary bases constructed from Laguerre-Gaussian (LG) modes with a fixed radial index of zero, it is shown that the superposed joint-two-LG-mode (JTLGM) correlation function plays a fundamental role in determining the turbulence-induced mutual-unbiasedness decay. The mutual information between the sent and detected photonic states is used as a metric to quantify the degree of turbulence-induced mutual-unbiasedness decay. It is found that the degree of turbulence-induced mutual-unbiasedness decay depends on the scaled atmospheric coherence width, anisotropy of turbulence and contents of the complementary bases, and it can become non-negligible in certain cases.