Logarithmic light cone, slow entanglement growth and scrambling, and
quantum memory
- URL: http://arxiv.org/abs/2305.08334v2
- Date: Tue, 25 Jul 2023 11:42:24 GMT
- Title: Logarithmic light cone, slow entanglement growth and scrambling, and
quantum memory
- Authors: Yu Zeng, Alioscia Hamma, Yu-Ran Zhang, Qiang Liu, Rengang Li, Heng Fan
and Wu-Ming Liu
- Abstract summary: We derive a mechanism for the emergence and consequences of a logarithmic light cone (LLC)
As an application in quantum information processing, the LLC supports long-lived quantum memory after unitary time evolution.
- Score: 23.25245158672699
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Effective light cones may emerge in non-relativistic local quantum systems
from the Lieb-Robinson bounds, resulting in exponentially decaying commutator
norms of two space-time separated operators in the Heisenberg picture. Here, we
derive a mechanism for the emergence and consequences of a logarithmic light
cone (LLC). As a possible way, the LLC can emerge from a phenomenological model
of many-body-localization. We show that the information scrambling is
logarithmically slow in the regime of the LLC. We prove that the bipartite
entanglement entropy grows logarithmically with time for arbitrary finite space
dimensions and arbitrary initial pure states. As an application in quantum
information processing, the LLC supports long-lived quantum memory after
unitary time evolution: a quantum code with macroscopic code distance and
exponentially long lifetime.
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