This Letter demonstrates for chaotic maps [logistic, classical, and quantum standard maps (SMs)] that the exponential growth rate ($\mathrm{\Lambda }$) of the out-of-time-ordered four-point correlator is equal to the classical Lyapunov exponent ($\lambda$) plus fluctuations (${\mathrm{\Delta }}^{\left(\mathrm{fluc}\right)}$) of the one-step finite-time Lyapunov exponents (FTLEs). Jensen's inequality provides the upper bound $\lambda \le \mathrm{\Lambda }$ for the considered systems. Equality is restored with $\mathrm{\Lambda }=\lambda +{\mathrm{\Delta }}^{\left(\mathrm{fluc}\right)}$, where ${\mathrm{\Delta }}^{\left(\mathrm{fluc}\right)}$ is quantified by $k$-higher-order cumulants of the (covariant) FTLEs. Exact expressions for $\mathrm{\Lambda }$ are derived and numerical results using $k=20$ furnish ${\mathrm{\Delta }}^{\left(\mathrm{fluc}\right)}\sim ln\left(\sqrt{2}\right)$ for all maps (large kicking intensities in the SMs).

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• Chaos
• Quantum chaos
• Quantum chaotic systems
• Quantum kicked rotor