Quantum-information interpretation of generalized temporal entropies

Determine a rigorous quantum-information-theoretic interpretation of the complex-valued generalized temporal entropies defined from time-like cuts of the path integral via reduced transition matrices in 1+1-dimensional conformal field theories and related quench dynamics, clarifying what information-theoretic quantities these entropies correspond to and how they operationally relate to state complexity or correlations.

Background

The paper introduces generalized temporal entropies obtained by studying reduced transition matrices associated with time-like cuts in the path integral and by analytic continuation of twist-field correlators. These entropies are complex-valued and have been connected to geometric quantities in holographic field theories.

While the authors derive CFT predictions for the scaling of these entropies and validate them numerically with tensor networks, they note that a clear quantum information interpretation—i.e., what operational or information-theoretic meaning these complex entropies hold—has not been settled.

References

These complex-valued entropies are known to carry geometric information in holographic field theories where they have first been proposed but their interpretation in a quantum information context is still unclear.

— Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point  (2405.14706 - Carignano et al., 2024) in Abstract (p. 1) and Introduction (Section 1)

Alternative approaches reconstruct black-hole interiors from holographic complexity or pole-skipping data; a systematic comparison with the present TEE framework is left for future work.

— Metric Reconstruction from Timelike Entanglement Entropy  (2608.16517 - Feng et al., 17 Aug 2026) in Conclusion and Discussion, footnote to the paragraph beginning “The two prescriptions also differ in their access to the black-hole interior.”