Out-of-Time-Order Correlator Spectroscopy

• URL: http://arxiv.org/abs/2511.22654v1
• Date: Thu, 27 Nov 2025 17:42:51 GMT
• Title: Out-of-Time-Order Correlator Spectroscopy
• Authors: Keisuke Fujii,
• Abstract summary: We show that higher-order OTOCs fit within the framework of quantum signal processing.<n>We further generalize higher-order OTOCs by transformation of the singular values of the spatially resolved truncated propagator.<n>This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.
• Score: 3.9083778058145864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each $\mathrm{OTOC}^{(k)}$ measures the $2k$-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.

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