Phase Squeezing of Quantum Hypergraph States

Ramita Sarkar; Supriyo Dutta; Subhashish Banerjee; Prasanta K. Panigrahi

doi:10.1088/1361-6455/ac02d2

paper

Phase Squeezing of Quantum Hypergraph States

arXiv:2009.01082 · doi:10.1088/1361-6455/ac02d2

Abstract

Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $∣ G ⟩ = \frac{1}{2 ^{d}} \sum_{n = 0}^{2^{d} - 1} (- 1)^{f (n)} ∣ n ⟩$ , where $f$ is a $d$ -variable Boolean function depending on the hypergraph $G$ , and $∣ n ⟩$ 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 ${∣ n ⟩ : n = 0, 1, \dots (2^{d} - 1)}$ . 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.

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