Hou Zhibo, Xiang Guoyong, Dong Daoyi, Li Chuan-Feng, Guo Guang-Can
Opt Express. 2015 Apr 20;23(8):10018-31. doi: 10.1364/OE.23.010018.
We consider the problem of implementing mutually unbiased bases (MUB) for a polarization qubit with only one wave plate, the minimum number of wave plates. We show that one wave plate is sufficient to realize two MUB as long as its phase shift (modulo 360°) ranges between 45° and 315°. It can realize three MUB (a complete set of MUB for a qubit) if the phase shift of the wave plate is within [111.5°, 141.7°] or its symmetric range with respect to 180°. The systematic error of the realized MUB using a third-wave plate (TWP) with 120° phase is calculated to be a half of that using the combination of a quarter-wave plate (QWP) and a half-wave plate (HWP). As experimental applications, TWPs are used in single-qubit and two-qubit quantum state tomography experiments and the results show a systematic error reduction by 50%. This technique not only saves one wave plate but also reduces the systematic error, which can be applied to quantum state tomography and other applications involving MUB. The proposed TWP may become a useful instrument in optical experiments, replacing multiple elements like QWP and HWP.
我们考虑仅用一个波片（波片数量最少）为偏振量子比特实现相互无偏基（MUB）的问题。我们表明，只要其相移（模360°）在45°到315°之间，一个波片就足以实现两个MUB。如果波片的相移在[111.5°，141.7°]范围内或其相对于180°的对称范围内，则它可以实现三个MUB（量子比特的一组完整MUB）。计算得出，使用相移为120°的第三波片（TWP）实现的MUB的系统误差是使用四分之一波片（QWP）和半波片（HWP）组合时的一半。作为实验应用，TWP用于单量子比特和双量子比特量子态层析成像实验，结果表明系统误差降低了50%。该技术不仅节省了一个波片，还降低了系统误差，可应用于量子态层析成像及其他涉及MUB的应用。所提出的TWP可能会成为光学实验中的一种有用仪器，取代诸如QWP和HWP等多个元件。
