[2203.10501] Quantum Fluctuation-Response Inequality and Its Utility in Quantum Speculation Testing

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Summary:We set up a basic quantum fluctuation-response inequality that bounds the distinction in expectation values of an observable between two quantum states by way of the quantum relative entropy. For observables with bounded spectra, we additional strengthen this outcome by exploiting the sub-Gaussian property, and explicitly relate our certain to the sub-Gaussian norm of the observable. This enables us to derive a novel non-asymptotic certain on the sum of statistical errors in quantum speculation testing, which enhances and will be extra informative than current bounds. We additionally show the flexibility of our outcomes by issues corresponding to thermodynamic speculation testing and quantum pace limits in physics, and generalizability of algorithms in machine studying.