Dipartimento di Fisica, Sapienza Università di Roma, Roma 00185, Italy.
Sci Rep. 2013 Sep 25;3:2726. doi: 10.1038/srep02726.
In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a "qusix"), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution.
在量子信息中，量子力学可观测量的互补性起着关键作用。两个互补可观测量的本征态形成一对相互无偏的基（MUB）。更一般地说，一组 MUB 由所有两两无偏的基组成。除了希尔伯特空间的特定维度外，通常情况下，最大的 MUB 集是未知的。即使在像六这样低的维度，最大的 MUB 集的识别仍然是一个悬而未决的问题，尽管有强烈的数值证据表明，不存在三个以上的同时 MUB。在这里，我们利用新开发的全息技术，实现并测试了单光子六维量子态（"qusix"）的三组不同的 MUB，该量子态利用光子的偏振和轨道角动量进行编码。在理论和实验之间观察到了非常吻合的结果。我们的结果可以应用于态层析成像、定量波粒二象性、量子密钥分发。
