论文标题
量子超图状态的相位挤压
Phase Squeezing of Quantum Hypergraph States
论文作者
论文摘要
与$ D $顶点的HyperGraph $ G $对应，量子超图状态由$ | g \ rangle = \ frac {1} {\ sqrt {\ sqrt {2^d}} \ sum_ {n = 0} $ d $ - 可变布尔功能取决于HyperGraph $ g $，$ | n \ rangle $表示二进制为$ 2^d $的二进制矢量，$ 1 $，$ 1 $ at $ n $ th $ n $ th-th $ n = 0，1，\ dots（2^d-1）$。研究了这些状态的非古典特性。我们考虑在数量上作用于数字的$ 2^d $上的Hilbert Space上的an灭和创建操作员$ \ {| n \ rangle：n = 0，1，\ dots（2^d -1）\} $。在有限的维度上构建了Hermitian编号和相位操作员。这些状态的数量不确定性导致相挤压的概念。我们确定仅在相位正交中挤压这些状态，并满足非经典性的agarwal-tara标准，这仅取决于超图的顶点的数量。我们还指出，在相位正交中观察到相干性。
Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the hypergraph $G$, and $|n \rangle$ denotes a binary vector of length $2^d$ with $1$ at $n$-th position for $n = 0, 1, \dots (2^d - 1)$. The non-classical properties of these states are studied. We consider annihilation and creation operator on the Hilbert space of dimension $2^d$ acting on the number states $\{|n \rangle: n = 0, 1, \dots (2^d - 1)\}$. The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal-Tara criterion for non-classicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.
