论文标题
一般量子运动系统的高斯量子信息I：高斯状态
Gaussian quantum information over general quantum kinematical systems I: Gaussian states
论文作者
论文摘要
我们在具有有限的自由度有限的通用量子运动系统上开发了高斯国家的理论。基本相位空间由本地紧凑的Abelian（LCA）组$ G $描述，其符号结构由$ G $上的2 cocycle确定。我们利用伯恩斯坦（Bernstein）在LCA组上使用高斯分布的概念来定义高斯国家，并完全表征高斯状态在2个规则的LCA组上的$ g = f = f \ times \ hat {f} $，并带有规范的2个归一化2 cocycle。尤其涵盖了$ n $ bosonic模式的情况，$ n $ QUDIT系统具有奇数$ d \ ge 3 $，以及$ p $ - 亚种量子系统。当我们将量子运动系统分解为欧几里得部分和其余部分时，我们的表征揭示了对高斯国家纠缠的拓扑阻塞（其相位空间接收一个紧凑的开放亚组）。然后，我们将离散的Hudson定理\ cite {gro}概括为完全断开的2个常规LCA组的情况。我们还检查具有相位空间的角度数字系统$ \ MATHBB {t}^n \ times \ Mathbb {z}^n $和带有相位空间$ \ Mathbb {z}^{2n} {2n} _2 $（不是2个注册）的fermionic/硬核波索克系统，并完全表征他们的争座状态。
We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact abelian (LCA) group $G$ with a symplectic structure determined by a 2-cocycle on $G$. We use the concept of Gaussian distributions on LCA groups in the sense of Bernstein to define Gaussian states and completely characterize Gaussian states over 2-regular LCA groups of the form $G= F\times\hat{F}$ endowed with a canonical normalized 2-cocycle. This covers, in particular, the case of $n$-bosonic modes, $n$-qudit systems with odd $d\ge 3$, and $p$-adic quantum systems. Our characterization reveals a topological obstruction to Gaussian state entanglement when we decompose the quantum kinematical system into the Euclidean part and the remaining part (whose phase space admits a compact open subgroup). We then generalize the discrete Hudson theorem \cite{Gro} to the case of totally disconnected 2-regular LCA groups. We also examine angle-number systems with phase space $\mathbb{T}^n\times\mathbb{Z}^n$ and fermionic/hard-core bosonic systems with phase space $\mathbb{Z}^{2n}_2$ (which are not 2-regular), and completely characterize their Gaussian states.
