Vertex-minor universal graphs for generating entangled quantum subsystems

• URL: http://arxiv.org/abs/2402.06260v3
• Date: Tue, 14 May 2024 13:51:51 GMT
• Title: Vertex-minor universal graphs for generating entangled quantum subsystems
• Authors: Maxime Cautrès, Nathan Claudet, Mehdi Mhalla, Simon Perdrix, Valentin Savin, Stéphan Thomassé,
• Abstract summary: We study the notion of $k$-stabilizer universal quantum state, that is, an $n$-qubit quantum state, such that it is possible to induce any stabilizer state on any $k$ qubits. These states generalize the notion of $k$-pairable states introduced by Bravyi et al., and can be studied from a perspective using graph states and $k$-vertex-minor universal graphs.
• Score: 3.1758167940451987
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the notion of $k$-stabilizer universal quantum state, that is, an $n$-qubit quantum state, such that it is possible to induce any stabilizer state on any $k$ qubits, by using only local operations and classical communications. These states generalize the notion of $k$-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and $k$-vertex-minor universal graphs. First, we demonstrate the existence of $k$-stabilizer universal graph states that are optimal in size with $n=\Theta(k^2)$ qubits. We also provide parameters for which a random graph state on $\Theta(k^2)$ qubits is $k$-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of $k$-stabilizer universal graph states on $n = O(k^4)$ qubits. Both rely upon the incidence graph of the projective plane over a finite field $\mathbb{F}_q$. This provides a major improvement over the previously known explicit construction of $k$-pairable graph states with $n = O(2^{3k})$, bringing forth a new and potentially powerful family of multipartite quantum resources.

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