Lieb-Robinson Light Cone for Power-Law Interactions.

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Dynamics

Background:

• The Lieb-Robinson theorem establishes finite speed limits for information propagation in quantum systems with nearest-neighbor interactions.
• Understanding these limits is crucial for quantum communication and computation.

Purpose of the Study:

• To determine the speed limits of quantum information propagation in systems with power-law interactions.
• To establish optimal Lieb-Robinson bounds for quantum information dynamics with decaying interactions.

Main Methods:

• Analysis of quantum systems with interactions decaying as 1/r^{α} at distance r.
• Derivation of theoretical bounds applicable to all spatial dimensions d and exponents α>2d.

Main Results:

• Information propagation time scales as at least r^{min{1,α-2d}} over distance r.
• These derived bounds are shown to be saturable by recent state transfer protocols.

Conclusions:

• This work provides a definitive answer to the speed limits of quantum information propagation with power-law interactions.
• The established bounds are optimal and have significant implications for quantum information dynamics.