The SIC Question: History and State of Play

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.Comment: 16 pages, 1 figure, many references; v3: updating bibliography, dimension eight hundred forty fou

Design and characterization of optical-THz phase-matched traveling-wave photomixers

Design and characterization of optical-THz phase-matched traveling-wave photomixers for difference-frequency generation of THz waves are presented. A de-biased coplanar stripline fabricated on low-temperature-grown GaAs is illuminated by two non-collinear laser beams which generate moving interference fringes that are accompanied by THz waves. By tuning the offset angle between the two laser beams, the velocity of the interference fringe can be matched to the phase velocity of the THz wave in the coplanar stripline. The generated THz waves are radiated into free space by the antenna at the termination of the stripline. Enhancement of the output power was clearly observed when the phase-matching condition was satisfied. The output power spectrum has a 3-dB bandwidth of 2 THz and rolls off as ~9 dB/Oct which is determined by the frequency dependent attenuation in the stripline, while the bandwidth of conventional photomixer design has the limitation by the RC time constant due to the electrode capacitance. The device can handle the laser power of over 380 mW, which is 5 times higher than the maximum power handring capability of conventional small area devices. The results show that the traveling-wave photomixers have the potential to surpass small area designs, especially at higher frequencies over I THz, owing to their great thermal dissipation capability and capacitance-free wide bandwidth

A traveling-wave THz photomixer based on angle-tuned phase matching

A traveling-wave THz photomixer based on a free-space optical-THz phase-matching scheme is proposed. A dc-biased coplanar strip line fabricated on low-temperature-grown GaAs serves as the active area of the device, and is illuminated by two noncollinear laser beams which generate interference fringes that are accompanied by THz waves. The device with the laser-power-handling capability over 300 mW and a 3-dB bandwidth of 1.8 THz was experimentally demonstrated. The results show that traveling-wave photomixers have the potential to surpass small-area designs