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Physics

Analytic Continuation Between Real- and Imaginary-Time Quantum Dynamics and the Fundamental Instability of Inverse Reconstruction

Pengfei Zhu

Featured May 17, 2026

Original Paper

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Simply

Imaginary-time quantum evolution acts like a special filter that smooths out fast changes, making it hard to perfectly reverse and see the original quick movements; this paper shows exactly how much detail can still be recovered.

In depth
The paper introduces a unified spectral-semigroup framework that connects real-time and imaginary-time quantum dynamics. It demonstrates that imaginary-time evolution acts as an effective fractional low-pass filter, suppressing high-frequency components. This framework quantifies a recoverability bound, showing that only low-energy dynamical features can be stably reconstructed from imaginary-time data, thus defining the limits of information recovery.

Key Takeaways

  • 1
    A unified spectral-semigroup framework is developed, recasting imaginary-time evolution as a fractional low-pass filter generated by a square-root operator.
  • 2
    The inverse problem of reconstructing real-time dynamics from imaginary-time data is fundamentally ill-posed, but a recoverability bound quantifies which spectral modes can be stably recovered.
  • 3
    The study establishes a scale-dependent asymmetry in information recovery, where low-energy features are reconstructable, but high-frequency components are exponentially unstable under inversion.

Conceptual Flow

HIGH LEVEL
1
Methodology: How Real and Imaginary Time Connect

The paper shows how to link real-time quantum movements (like waves) to imaginary-time changes (like heat spreading) using a special mathematical filter.

Real Time Movement
Apply Special Filter
Imaginary Time Change
2
Results: What Can Be Recovered?

They found that only the slow, big patterns from the imaginary-time changes can be reliably turned back into real-time movements, while fast, tiny details are lost.

Imaginary Time Data
Some Noise
Try to Reconstruct
Recovered Slow Patterns
Lost Fast Details