Vertex-minor universal graphs for generating entangled quantum subsystems
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917778839044096 |
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| author | Cautrès, Maxime Claudet, Nathan Mhalla, Mehdi Perdrix, Simon Savin, Valentin Thomassé, Stéphan |
| author_facet | Cautrès, Maxime Claudet, Nathan Mhalla, Mehdi Perdrix, Simon Savin, Valentin Thomassé, Stéphan |
| contents | 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 $n=Θ(k^2)$ qubits. We also provide parameters for which a random graph state on $Θ(k^2)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vertex-minor universal graphs for generating entangled quantum subsystems Cautrès, Maxime Claudet, Nathan Mhalla, Mehdi Perdrix, Simon Savin, Valentin Thomassé, Stéphan Quantum Physics Discrete Mathematics 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 $n=Θ(k^2)$ qubits. We also provide parameters for which a random graph state on $Θ(k^2)$ 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. |
| title | Vertex-minor universal graphs for generating entangled quantum subsystems |
| topic | Quantum Physics Discrete Mathematics |
| url | https://arxiv.org/abs/2402.06260 |