aiqbench analysis
This is a theoretical quantum-optics study of how different distance measures rank the relaxation of two Gaussian states in a driven oscillator, and the measures can disagree about which state converges first. The result is a foundational point about how the choice of diagnostic and observation window determines whether a Mpemba reversal counts as "lasting." Its direct relevance is to quantum state characterization and to devices like parametric amplifiers, which are used in quantum sensing and readout, but it is not an experimental or engineering result.
Diagnostic-dependent lasting Mpemba effect in a parametrically driven oscillator
arXiv:2610.36663v1 Announce Type: new Abstract: For two Gaussian preparations of a detuned degenerate parametric amplifier below threshold, the trace distance shows a lasting Mpemba reversal, whereas the relative entropy eventually restores the initial order and the Hilbert--Schmidt distance alternates indefinitely. All three diagnostics agree on the initial order, and these orders persist on open sets of preparations and quadratic generators. The disagreement is possible because a real relaxation mode and a complex-conjugate pair share the leading decay rate, a coincidence that holds for any single-mode quadratic oscillator with linear damping in the elliptic regime. Number symmetry hides their competition in the undriven trace-distance tail, and parametric driving exposes it. Near a pure stationary state, the relative entropy strongly weights changes of the symplectic eigenvalue, which approximately follow the nonoscillating energy deviation; thermal occupation weakens this preference. A first-order splitting rule shows that weak number dephasing and two-photon loss favor the real branch, whereas a Kerr interaction with the same sign as the detuning favors the pair. We quantify the thermal-occupation and dephasing tolerances and estimate the measurement precision needed to observe the disagreement. Whether a Mpemba reversal is lasting therefore depends on the diagnostic and on the observation window.
Abstract:For two Gaussian preparations of a detuned degenerate parametric amplifier below threshold, the trace distance shows a lasting Mpemba reversal, whereas the relative entropy eventually restores the initial order and the Hilbert--Schmidt distance alternates indefinitely. All three diagnostics agree on the initial order, and these orders persist on open sets of preparations and quadratic generators. The disagreement is possible because a real relaxation mode and a complex-conjugate pair share the leading decay rate, a coincidence that holds for any single-mode quadratic oscillator with linear damping in the elliptic regime. Number symmetry hides their competition in the undriven trace-distance tail, and parametric driving exposes it. Near a pure stationary state, the relative entropy strongly weights changes of the symplectic eigenvalue, which approximately follow the nonoscillating energy deviation; thermal occupation weakens this preference. A first-order splitting rule shows that weak number dephasing and two-photon loss favor the real branch, whereas a Kerr interaction with the same sign as the detuning favors the pair. We quantify the thermal-occupation and dephasing tolerances and estimate the measurement precision needed to observe the disagreement. Whether a Mpemba reversal is lasting therefore depends on the diagnostic and on the observation window.
arXiv:2610.36663 [quant-ph]
(or arXiv:2610.36663v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.36663 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 285 words