Effect of entanglement on geometric phase for multi-qubit states

TL;DR

This paper investigates how entanglement influences the geometric phase in multi-qubit states, revealing that certain states' phase corrections are fully characterized by either entanglement or classical correlations, with implications for quantum gauge fields.

Contribution

It demonstrates that the entanglement correction to the geometric phase can be completely characterized by entanglement or classical correlations for specific multi-qubit states.

Findings

Entanglement fully characterizes phase correction in W states.

Classical correlations characterize phase correction in GHZ and cluster states.

The structure of these states is analyzed using local invariants and the twist gauge field.

Abstract

When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state's projective Hilbert space. A correction term to this geometric phase in addition to the local subsystem phases may appear from correlations between the subsystems. We find this correction term can be characterized completely either by the entanglement or completely by the classical correlations for several classes of entangled state. States belonging to the former set are W states and their mixtures, while members of the latter set are cluster states, GHZ states and two classes of bound entangled state. We probe the structures of these states more finely using local invariants and suggest the cause of the entanglement correction is a gauge field like $SL(2,\mathbb{C})$ invariant recently introduced named twist.