Entanglement transitions induced by large deviations

Area of Science:

• Quantum Information Theory
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Bipartite quantum systems are fundamental to quantum information.
• Schmidt eigenvalues characterize entanglement in bipartite systems.
• Large deviations in quantum systems can alter entanglement properties.

Purpose of the Study:

• To analytically compute the probability of large deviations for the smallest Schmidt eigenvalue.
• To investigate the impact of these deviations on bipartite entanglement measures.
• To develop and validate a random matrix model for entanglement transitions.

Main Methods:

• Coulomb gas method for calculating deviation probabilities.
• Von Neumann entropy to study bipartite entanglement.
• Analysis of the density matrix's partial transpose (ρ_{12}^{Γ}).
• Log negativity for quantifying entanglement.

Main Results:

• The probability of large deviations follows exp[-βN^{2}Φ(ζ)], with an exactly calculated rate function Φ(ζ).
• Large deviations significantly affect bipartite entanglement and entanglement in further partitioned subsystems.
• A random matrix model accurately captures entanglement properties and predicts a transition at a critical large deviation parameter (ζ).

Conclusions:

• The Coulomb gas method provides an exact solution for large deviation rate functions.
• Extreme eigenvalue fluctuations play a crucial role in determining bipartite entanglement.
• The developed random matrix model offers a powerful tool for understanding entanglement transitions in quantum systems.