The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement

TL;DR

This paper explores the control landscape of quantum state transitions in multi-qubit systems driven by single-qubit unitaries, analyzing the landscape features, entanglement measures, and the ability to reach Schmidt states via gradient flow.

Contribution

It provides a full analysis of the two-qubit control landscape, including the nature of extrema and saddle points, and extends the approach to multi-qubit systems with implications for entanglement measurement.

Findings

Two-qubit landscape has no traps, with identifiable maxima, minima, and saddle points.

Gradient flow can locate Schmidt states from arbitrary two-qubit states.

Relation established between Schmidt states and Bures distance-based entanglement measure.

Abstract

This paper considers the control landscape of quantum transitions in multi-qubit systems driven by unitary transformations with single-qubit interaction terms. The two-qubit case is fully analyzed to reveal the features of the landscape including the nature of the absolute maximum and minimum, the saddle points and the absence of traps. The results permit calculating the Schmidt state starting from an arbitrary two-qubit state following the local gradient flow. The analysis of multi-qubit systems is more challenging, but the generalized Schmidt states may also be located by following the local gradient flow. Finally, we show the relation between the generalized Schmidt states and the entanglement measure based on the Bures distance.