Lieb-Robinson bound and locality for general markovian quantum dynamics

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Quantum Dynamics

Background:

• The Lieb-Robinson bound establishes a maximum speed for signal propagation in quantum systems with local interactions.
• This concept extends relativistic causality beyond quantum field theory, proving crucial for condensed matter and quantum information.
• Existing bounds primarily apply to specific quantum evolutions, limiting broader applications.

Purpose of the Study:

• To generalize the Lieb-Robinson bound to encompass general Markovian quantum evolution.
• To establish an equivalent bound for a wider range of quantum systems.
• To utilize the generalized bound to analyze correlation decay in stationary states of Markov processes.

Main Methods:

• Mathematical derivation of a generalized Lieb-Robinson bound for Markovian quantum dynamics.
• Analysis of correlation functions in the stationary state of quantum Markov processes.
• Relating correlation decay length scale to the Lieb-Robinson velocity and system relaxation time.

Main Results:

• An equivalent Lieb-Robinson bound is proven to hold for general Markovian quantum evolution.
• Correlations in the stationary state of a Markov process exhibit decay.
• The decay length scale of these correlations is determined by the Lieb-Robinson velocity and the system's relaxation time.

Conclusions:

• The Lieb-Robinson bound's applicability is significantly extended to general Markovian quantum systems.
• This provides a powerful tool for understanding causality and information propagation in diverse quantum settings.
• The study reveals fundamental relationships between quantum dynamics, causality, and correlation decay.