Planat Michel, Gedik Zafer
Université de Bourgogne/Franche-Comté, Institut FEMTO-ST CNRS UMR 6174, 15 B Avenue des Montboucons, 25044 Besançon, France.
Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey.
R Soc Open Sci. 2017 Sep 6;4(9):170387. doi: 10.1098/rsos.170387. eCollection 2017 Sep.
Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such informationally complete POVMs, investigated in dimensions 2-12, exhibit simple finite geometries in their projector products and, for dimensions 4 and 8 and 9, relate to two-qubit, three-qubit and two-qutrit contextuality.
置换门的本征态要么是稳定子态（对于泡利群中的门），要么是魔法态，从而实现通用量子计算（普拉纳特、鲁赫桑 - 乌尔 - 哈克，《高等数学物理》2017年，5287862（doi:10.1155/2017/5287862））。我们在本文中表明，这类魔法态的一个子集作用于广义泡利群时，会定义（不对称的）信息完备正算子值测量（POVM）。在2至12维中研究的此类信息完备POVM，在其投影算子乘积中展现出简单的有限几何结构，并且对于4维、8维和9维，与两量子比特、三量子比特和两量子三态的背景相关性有关。
