Generalized Loschmidt echo and information scrambling in open systems

Quantum information scrambling, typically explored in closed quantum systems, describes the spread of initially localized information throughout a system and can be quantified by measures such as the Loschmidt echo (LE) and out-of-time-order correlator (OTOC). In this paper, we explore information scrambling in the presence of dissipation by generalizing the concepts of LE and OTOC to open quantum systems governed by Lindblad dynamics. We investigate the universal dynamics of the generalized LE across regimes of weak and strong dissipation. In the weak dissipation regime, we identify a universal structure, while in the strong dissipation regime, we observe a distinctive two-local-minima structure, which we interpret through an analysis of the Lindblad spectrum. Furthermore, we establish connections between the thermal averages of LE and OTOC and prove a general relation between OTOC and Rényi entropy in open systems. Finally, we propose an experimental protocol for measuring OTOC in open systems. These findings provide deeper insights into information scrambling under dissipation and pave the way for experimental studies in open quantum systems.

💡 Research Summary

This paper extends two central diagnostics of quantum information scrambling—Loschmidt echo (LE) and out‑of‑time‑order correlator (OTOC)—to open quantum systems governed by Lindblad master equations. By mapping a density matrix onto a doubled‑space wavefunction via the Choi‑Jamiolkowski isomorphism, the authors rewrite the Lindblad dynamics as a non‑Hermitian Schrödinger‑like evolution with a double‑space Hamiltonian H_D = H_s – i H_d. The generalized LE is defined as the normalized Hilbert‑Schmidt overlap M_D(t)=Tr