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arXiv · 2512.02976

Many-body $k$-local ground states as probes for unitary quantum metrology

Majid Hassani·Mengyao Hu·Guillem Müller-Rigat·Matteo Fadel·Jordi Tura
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Abstract

Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared. On the other hand, experimentally practical Hamiltonians often involve few-body correlators only. Here, we study the metrological performances under this constraint, using tools derived from the quantum Fisher information. Our work applies to any encoding generator, also including a dependence on the parameter. We find that typical random symmetric ground states of $k$-body permutation-invariant Hamiltonians exhibit Heisenberg scaling. Finally, we establish a tradeoff between the Hamiltonian's gap, which quantifies preparation hardness, and the quantum Fisher information of the corresponding ground state.

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Majid Hassani, Mengyao Hu, Guillem Müller-Rigat, Matteo Fadel, Jordi Tura. 2025-12-02. Many-body $k$-local ground states as probes for unitary quantum metrology. https://arxiv.org/abs/2512.02976

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