TL;DR
This paper reviews the role of geometric phases in quantum information, highlighting their applications in robust quantum computation, extensions to mixed states, and new topological phases in entangled systems, supported by recent experiments.
Contribution
It provides a comprehensive overview of recent theoretical and experimental advances in geometric phases within quantum information science, emphasizing new topological phases and mixed state concepts.
Findings
Geometric phases enable robust quantum computation.
Development of geometric phase concepts for mixed states.
Discovery of new topological phases in entangled systems.
Abstract
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by focusing on three main themes: the use of GPs to perform robust quantum computation, the development of GP concepts for mixed quantum states, and the discovery of a new type of topological phases for entangled quantum systems. We delineate the theoretical development as well as describe recent experiments related to GPs in the context of quantum information.
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