Phase Squeezing of Quantum Hypergraph States

• URL: http://arxiv.org/abs/2009.01082v1
• Date: Mon, 31 Aug 2020 18:31:13 GMT
• Title: Phase Squeezing of Quantum Hypergraph States
• Authors: Ramita Sarkar, Supriyo Dutta, Subhashish Banerjee, Prasanta K. Panigrahi
• Abstract summary: A quantum hypergraph state is defined by $|Grangle = frac1sqrt2dsum_n = 02d - 1 (-1)f(n) |n rangle$. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal-Tara criterion for non-classicality.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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