Symmetry hinders quantum information recovery
Hiroyasu Tajima, Keiji Saito · arXiv (Cornell University) · 2021
Quantum information is scrambled via a chaotic time evolution in many-body systems. Clarifying how and to what extent we can recover the quantum information from the scrambled state is a central issue of today's physics, since it commonly appears as an essential factor in various topics including irreversibility of quantum chaotic dynamics, fault-tolerant quantum computation, and black hole information paradox. In realistic settings, symmetry can ubiquitously exist in scrambling dynamics. Here we establish fundamental limitations on the information recovery arising from the Lie group symmetries in the scrambling dynamics. The results are applicable to many situations, including the Hayden-Preskill black hole model with symmetry where the success rate of the information recovery qualitatively changes from the original no-symmetry case. Our findings show a close relationship between information recovery, symmetry, and quantum coherence, and that symmetry hinders the quantum information recovery.