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This paper links the spectral form factor, a standard diagnostic of quantum chaos, to quantum Fisher information measured through quantum sensing protocols. It argues that the resulting quantity self-averages, so it is less noisy to measure than the SFF itself. The work is mainly theoretical quantum physics with a sensing-based route to experimental access, so it is relevant to quantum technology readers but not to near-term applications.
Probe Signatures of Quantum Chaos with Quantum Sensing
arXiv:2610.16181v1 Announce Type: new Abstract: The spectral form factor (SFF), which is the Fourier transform of the two-point spectral correlation, is a fundamental diagnostics of quantum chaos. Nevertheless, its experimental detection in quantum many-body systems was less unexplored until recently. Here, we establish a relationship between the SFF with the quantum Fisher information (QFI) by means of quantum sensing protocols. Furthermore, when the eigenvalues and eigenstates of the disordered Hamiltonian are statistically independent, we prove that QFI is typical both in short and long timescales while numerics suggest that it is also typical at intermediate timescales, which ensures self-averaging of QFI. The self-averaging property renders the experimental measurement of QFI with our protocol less noisy in contrast with the direct measurement of SFF which is known to be non-self-averaging. Our results reveal an intriguing connection between quantum noise and the signatures of quantum chaos.
Abstract:The spectral form factor (SFF), which is the Fourier transform of the two-point spectral correlation, is a fundamental diagnostics of quantum chaos. Nevertheless, its experimental detection in quantum many-body systems was less unexplored until recently. Here, we establish a relationship between the SFF with the quantum Fisher information (QFI) by means of quantum sensing protocols. Furthermore, when the eigenvalues and eigenstates of the disordered Hamiltonian are statistically independent, we prove that QFI is typical both in short and long timescales while numerics suggest that it is also typical at intermediate timescales, which ensures self-averaging of QFI. The self-averaging property renders the experimental measurement of QFI with our protocol less noisy in contrast with the direct measurement of SFF which is known to be non-self-averaging. Our results reveal an intriguing connection between quantum noise and the signatures of quantum chaos.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph)
arXiv:2610.16181 [quant-ph]
(or arXiv:2610.16181v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.16181 arXiv-issued DOI via DataCite (pending registration)
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