Comment on "Geometric Phases for Mixed States in Interferometry"
Paul B. Slater (University of California)
TL;DR
This paper critically examines the relationship between Uhlmann's mathematical mixed state holonomy and the experimentally relevant geometric phase in quantum interferometry for spin-1/2 systems, highlighting their limited agreement.
Contribution
It clarifies the connection between mathematical and physical geometric phases, showing their limited correspondence in specific quantum evolutions.
Findings
Limited agreement between Uhlmann holonomy and interferometric geometric phase
Analysis focused on spin-1/2 systems undergoing geodesic evolution
Highlights differences in mathematical and experimental phase concepts
Abstract
We find for the unitary evolution of spin-1/2 systems that the "purely mathematical mixed state holonomy of Uhlmann limitedly agrees, in the case of evolution over geodesic spherical triangles, with the holonomy "in the experimental context of quantum interferometry" recently proposed by Sjoqvist, Pati, Ekert, Anandan, Ericsson, Oi and Vedral (Phys. Rev. Lett. 85 [2000], 2845-2848).
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Taxonomy
TopicsOptical Polarization and Ellipsometry · Advanced Measurement and Metrology Techniques · Optical measurement and interference techniques