论文标题
Pauli Group和对角线Clifford的奇数尺寸中的线性约束系统没有量子解决方案
No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
论文作者
论文摘要
事实证明，线性约束系统（LCS）在研究量子基础中的非经典相关性和各种相关问题的研究中已被证明是一种令人惊讶的多产工具。许多结果以布尔利亚案而闻名，但是对奇数尺寸系统的概括在很大程度上是开放的。特别是，尚不清楚是否存在奇数尺寸的LC，它可以接收有限的维量子，但没有经典的解决方案。在最近的工作中，[J。物理。 A，53，385304（2020）]表明，在布尔案例中，N Qubit Pauli组引起了LCS（例如Mermin-Peres Square）的量子溶液，NQudit Pauli Group从未引起LCS在奇数尺寸中的量子溶液。在这里，我们将此结果推广到Clifford层次结构。更确切地说，我们考虑了（单Qudit）Pauli和对角线Clifford操作员产生的群体的张量。
Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions. In recent work, [J. Phys. A, 53, 385304 (2020)] have shown that unlike in the Boolean case, where the n-qubit Pauli group gives rise to quantum solutions of LCS such as the Mermin-Peres square, the n-qudit Pauli group never gives rise to quantum solutions of a LCS in odd dimension. Here, we generalise this result towards the Clifford hierarchy. More precisely, we consider tensor products of groups generated by (single-qudit) Pauli and diagonal Clifford operators.
