Abstract
We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We present a ``membrane theory'' in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality after taking the large local Hilbert space dimension limit. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an $O(1)$ amount of information is found to be delocalized by local operators in free fermionic systems and random Clifford circuits.
Highlights
We study free fermions as an example of a noninteracting system
We find for Haar random unitary channels with large local Hilbert space dimensions that local information is entirely delocalized by the local operator, regardless of the operator chosen
The local operator entanglement of holographic twodimensional (2D) CFTs is studied in Sec
Summary
We study free fermions as an example of a noninteracting system. In particular, we consider the tight-binding Hamiltonian for simplicity. After the wave front of the operator leaves the subsystems, the BOMI begins to relax back to its initial value, though we do not have a proof that the BOMI fully relaxes back to its original value due to finite size effects. This O(1) change (not extensive with system size) in the BOMI is a signature of the noninteracting nature of free fermions. It is initially zero but decreases once the operator is within the subregion. The latetime behavior of TOMI indicates the lack of scrambling from operators in the free fermion system
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have