Phase Squeezing of Quantum Hypergraph States

TL;DR

This paper introduces phase squeezing in quantum hypergraph states, demonstrating their non-classical phase properties and coherence, with potential implications for quantum information processing.

Contribution

It constructs Hermitian number and phase operators for hypergraph states and shows these states exhibit phase squeezing and non-classicality based on hypergraph structure.

Findings

States are phase squeezed only in the phase quadrature

States satisfy the Agarwal-Tara non-classicality criterion

Coherence is observed in the phase quadrature

Abstract

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.