Asymptotic phase-locking and synchronization in two-qubit systems

TL;DR

This paper analytically classifies mechanisms of spontaneous phase-locking and synchronization in two-qubit systems under Lindbladian dynamics, exploring their structures, properties, and implications for information preservation and entanglement.

Contribution

It provides a comprehensive classification and detailed analysis of phase-locking mechanisms in two-qubit Lindbladian systems, including their structures and physical implications.

Findings

Identified all phase-locking-enforcing mechanisms within the framework.

Established an upper bound on oscillation amplitudes of phase-locked dynamics.

Rebutted entanglement as a phase-locking witness through analytical examples.

Abstract

The paper concerns spontaneous asymptotic phase-locking and synchronization in two-qubit systems undergoing continuous Markovian evolution described by Lindbladian dynamics with normal Lindblad operators. Using analytic methods, all phase-locking-enforcing mechanisms within the given framework are obtained and classified. Detailed structures of their respective attractor spaces are provided and used to explore their properties from various perspectives. Amid phase-locking processes those additionally enforcing identical stationary parts of both qubits are identified, including as a special case the strictest form of synchronization conceivable. A prominent basis is presented which reveals that from a physical point of view two main types of phase-locking mechanisms exist. The ability to preserve information about the initial state is explored and an upper bound on the amplitude of oscillations of the resulting phase-locked dynamics is established. Permutation symmetry of both asymptotic states and phase-locking mechanisms is discussed. Lastly, the possibility of entanglement production playing the role of a phase-locking witness is rebutted by three analytically treatable examples.