Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Many-Body Systems

Background:

• Understanding entanglement dynamics is crucial for characterizing quantum many-body systems.
• Quantum quenches probe non-equilibrium dynamics and entanglement evolution.
• Entanglement negativity and mutual information are key measures of quantum correlations.

Purpose of the Study:

• To derive an exact, universal relation for entanglement growth in a specific quantum system.
• To connect entanglement negativity with Rényi-1/2 mutual information.
• To establish the applicability of this relation to various quantum systems.

Main Methods:

• Utilizing a replica trick and space-time duality transformation.
• Analyzing a tripartite, one-dimensional many-body system after a quantum quench.
• Deriving an exact relationship valid for short times.

Main Results:

• An exact, universal relation between entanglement negativity and Rényi-1/2 mutual information was derived.
• This relation holds at times shorter than subsystem sizes.
• The derived relation is applicable to any local quantum circuit.

Conclusions:

• The study provides a powerful tool for analyzing entanglement in quantum many-body systems.
• The findings are relevant for understanding information propagation in quantum systems.
• The universality of the relation suggests broad applicability in quantum physics.