Corresponding to a hypergraph G with d vertices, a quantum hypergraph state is defined by , where f is a d-variable Boolean function depending on the hypergraph G, and denotes a binary vector of length 2 ^d with 1 at the nth position for n = 0, 1, …(2 ^d − 1). The nonclassical properties of these states are studied. We consider the annihilation and creation operator on the Hilbert space of dimension 2 ^d acting on the number states . 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 nonclassicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.

对应于一个超图ģ与d的顶点，量子超图状态由下式定义，其中˚F是d取决于超图-variable布尔函数G ^，和表示长度为2的二元载体^d在1 Ñ为个位置Ñ = 0, 1, …(2 ^d − 1)。研究了这些状态的非经典性质。我们考虑作用于数态的2 ^d维希尔伯特空间上的湮灭和创造算子 . 构造有限维数的 Hermitian 数和相位算子。这些状态的数量相位不确定性导致了相位压缩的想法。我们确定这些状态仅在相位正交中被压缩，并且满足非经典性的 Agarwal-Tara 标准，该标准仅取决于超图的顶点数。我们还指出在相位正交中观察到相干性。