Separable states and the geometric phases of an interacting two-spin system

TL;DR

This paper investigates conditions under which a separable two-spin system's geometric phase equals the sum of its subsystems' phases, highlighting the role of nonlocal interactions in quantum entanglement.

Contribution

It provides a necessary and sufficient condition for a separable state to remain separable, ensuring additive geometric phases in an interacting bipartite system.

Findings

Identifies conditions for separability preservation during evolution.

Shows when the geometric phase is additive for bipartite systems.

Analyzes a well-known physical model to illustrate these conditions.

Abstract

It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this paper, we illustrate this point by investigating a well known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.