Quantum sensing of even- versus odd-body interactions

• URL: http://arxiv.org/abs/2401.06729v2
• Date: Wed, 06 Nov 2024 14:05:22 GMT
• Title: Quantum sensing of even- versus odd-body interactions
• Authors: Aparajita Bhattacharyya, Debarupa Saha, Ujjwal Sen,
• Abstract summary: estimation of coupling strength of arbitrary-body encoding Hamiltonians provides a scaling that increases monotonically with an increase in the number of interacting particles. We find that Hamiltonians having odd-body interactions necessarily require genuine multipartite entanglement in probes to attain the best metrological precision. We provide an upper bound on the number of parties up to which one can always obtain an asymmetric product state that gives the best metrological precision for even-body interactions.
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• Abstract: We find that estimation of coupling strength of arbitrary-body encoding Hamiltonians provides a scaling that increases monotonically with an increase in the number of interacting particles, in the limit of large number of particles. We perform this analysis for two types of probes -- optimal symmetric product probes and optimal ones -- and find that this feature is prevalent in both the cases. Moreover, we also ask if genuine multiparty entanglement is indispensable in attaining the best metrological precision if we employ non-local terms in the Hamiltonian. We identify a dichotomy in the answer. Specifically, we find that Hamiltonians having odd-body interactions necessarily require genuine multipartite entanglement in probes to attain the best metrological precision, but the situation is opposite in the case of Hamiltonians with even-body interactions. The optimal probes corresponding to Hamiltonians that contain even-body interaction terms, may be entangled, but certainly not so in all bipartitions, and particularly, it is possible to attain optimal precision using asymmetric probes. Asymmetry, which therefore is a resource in this scenario rather than genuine multiparty entanglement, refers to the disparity between states of local parts of the global system. Thereby we find a complementarity in the requirement of asymmetry and genuine entanglement in optimal probes for estimating strength of odd- and even-body interactions respectively. Additionally, we provide an upper bound on the number of parties up to which one can always obtain an asymmetric product state that gives the best metrological precision for even-body interactions. En route, we find the quantum Fisher information in closed form for two- and three-body interactions for arbitrary number of parties. Further, we identify conditions on the Hamiltonian, for which these results hold for arbitrary local dimensions.

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